Investigation of High Frequency Switching Transients on Wind Turbine Step Up Transformers by Mantosh Devgan A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Applied Science in Electrical and Computer Engineering Waterloo, Ontario, Canada, 2015 ©Mantosh Devgan 2015
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Investigation of High Frequency
Switching Transients on Wind Turbine
Step Up Transformers
by
Mantosh Devgan
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Master of Applied Science
in
Electrical and Computer Engineering
Waterloo, Ontario, Canada, 2015
©Mantosh Devgan 2015
ii
AUTHOR'S DECLARATION
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any
required final revisions, as accepted by my examiners.
I understand that my thesis may be made electronically available to the public.
iii
Abstract
Pre-mature failures of wind turbine step up (WTSU) transformers have been reported in the wind
farms although, the failed transformers had previously passed all quality assurance tests and had
assembled all standard requirements. Vacuum circuit breaker (VCB) initiated steep front transient
impact is one of the potential causes of such insulation failures. The use of VCB as switching devices
and intense cable network increases the likelihood for high frequency transient overvoltages (TOVs)
in wind farms. Multiple prestrikes and restrikes of VCB in conjunction with cable capacitance and
inductance of transformer give rise to fast steep front voltage transients, which eventually cause
insulation failures in WTSU transformer. This emphasizes the need to conduct switching transient
analysis studies for wind power plants, to investigate the severe switching overvoltages experienced
by WTSU transformers. In this work, high frequency modeling in a broad frequency range for major
components of the wind farms and an investigation of switching transients on WTSU transformer are
presented. An adaptive model of VCB capable of simulating statistical phenomena and overvoltages
on circuit breaker and the components that it interacts with is developed in PSCAD/EMTDC. A high
frequency phase model of single core cable, taking into account the high frequency effect of cable,
i.e., electromagnetic transient propagation, skin effect and reflections is simulated in
PSCAD/EMTDC. A linear wideband frequency-dependent black box model of an actual WTSU
transformer based on the experimental determination of admittance matrix in a wide frequency range
and subjecting the measured admittance matrix to an approximation by means of a rational function
through vector fitting is used to simulate WTSU transformer. The rational function obtained for
WTSU transformer can then be realized into an RLC network for time domain simulations in
PSCAD/EMTDC. A test bench is simulated using the above mentioned high frequency models and
replicating Type-IV wind turbine generator synchronized with the grid. Transient scenarios are
investigated to understand the most severe switching transients experienced by WTSU transformers,
considering the worst repeated switching transient overvoltages and the steep rate of voltage rise
experienced by the WTSU transformer. Six different attributes of voltage waveforms across the
WTSU transformer are used to investigate the transient behavior in the cases carried out on the
proposed test bench.
iv
Acknowledgements
I am deeply in debt to my supervisor, Dr. Shesha Jayaram, without whose support and guidance the
completion of this thesis would not have been possible.
My deepest gratitude goes to all the members of my family, for the wonderful support they
provided; especially my mother, Mrs. Rama Kanta Sharma, my father Mr. Vijay Sharma and my
sister Swati Devgan.
I would like to thank Dr. Magdy Salama and Dr. Kankar Bhattacharya for being the readers of my
thesis.
Many thanks are due to my friends at HVEL, including Mahdi Khanali, Mohammad Saleh
Moonesan and Mohana Krishnan, for the wonderful time we spent together. Special thanks to my
great friend Shahryar Anjum, who supported me throughout this journey.
I dedicate this thesis to my parents, who are no less than GOD to me.
.
v
Table of Contents
AUTHOR'S DECLARATION ............................................................................................................... ii
Abstract ................................................................................................................................................. iii
Acknowledgements ............................................................................................................................... iv
Table of Contents ................................................................................................................................... v
List of Figures ..................................................................................................................................... viii
List of Tables ......................................................................................................................................... xi
Nomenclature ....................................................................................................................................... xii
Chapter 1 Introduction ............................................................................................................................ 1
1.1 Background .................................................................................................................................. 2
1.1.1 Renewable energy systems: An overview ............................................................................. 2
1.1.2 Evolution of wind energy ...................................................................................................... 3
1.1.3 Wind energy today in Ontario ............................................................................................... 4
1.2 Types and Typical Configurations of Wind Farm Generators ..................................................... 4
1.3 Wind Turbine Step-Up Transformers ........................................................................................... 8
1.4 Problems Associated with Wind Turbine Step-Up Transformers ................................................ 9
1.5 Thesis Organization .................................................................................................................... 12
Chapter 2 Literature Review ................................................................................................................ 14
2.1 Classification of Transient Overvoltage ..................................................................................... 14
2.1.1 Impulse transients ................................................................................................................ 14
2.1.2 Oscillatory transients ........................................................................................................... 14
2.1.3 Travelling waves ................................................................................................................. 15
2.2 Vacuum Circuit Breaker initiated high frequency transients ..................................................... 17
2.3 Overvoltage Transients Experienced in Cable Systems ............................................................. 21
2.4 High Frequency Transients in Wind Farms ................................................................................ 22
2.5 Occurrence and mitigation of switching transients .................................................................... 24
2.6 Problem Identification ................................................................................................................ 26
2.7 Research Objectives ................................................................................................................... 27
Chapter 3 High Frequency Models of Wind Power Components ........................................................ 28
3.1 Modeling of Vacuum Circuit Breaker in PSCAD/EMTDC ....................................................... 28
3.1.1 Explanation of physical phenomena within a VCB ............................................................. 29
3.1.2 Dielectric Strength Calculation ........................................................................................... 31
vi
3.1.3 High Frequency Current Quenching Capability ................................................................. 32
3.1.4 Simulation of restrike phenomena of VCB in a capacitive circuit ...................................... 33
3.1.5 VCB model in PSCAD/EMTDC ........................................................................................ 38
3.2 Cable Modeling .......................................................................................................................... 53
3.2.1 Layers of cable model in PSCAD/EMTDC ........................................................................ 55
3.2.2 Physical properties of the cable materials used ................................................................... 56
3.2.3 Matching the capacitance and inductance of the cable ....................................................... 56
3.3 Modeling of WTSU Transformer .............................................................................................. 57
3.3.1 Overview of Modeling Procedure ....................................................................................... 58
3.3.2 Rational approximation of frequency response by vector fitting ........................................ 60
3.3.3 Passivity enforcement on the fitted admittance matrix ....................................................... 62
3.3.4 Time domain implementation after passivity enforcement ................................................. 63
3.3.5 Final WTSU Transformer model in PSCAD/EMTDC ....................................................... 65
3.4 Summary .................................................................................................................................... 68
Chapter 4 VCB initiated switching transient analysis on Type IV Wind Farm ................................... 69
4.1 Test Bench Layout ..................................................................................................................... 69
4.1.1 Generation System: Doubly fed induction generator .......................................................... 70
4.1.2 Vacuum Circuit Breaker ..................................................................................................... 71
4.1.3 Cable ................................................................................................................................... 73
4.1.4 WTSU Transformer ............................................................................................................ 74
4.1.5 Collection grid .................................................................................................................... 75
4.2 Tools for classifying the switching transients ............................................................................ 76
4.3 VCB initiated switching transient test cases .............................................................................. 77
4.4 Elaboration of the test cases ....................................................................................................... 77
4.4.1 Case I: VCB opening on LV side of WTSU transformer under no load ............................ 78
4.4.2 Case II: VCB opening on LV side of WTSU transformer under an inductive load............ 79
4.4.3 Case III: VCB closing on LV side of WTSU transformer under no load ........................... 81
4.4.4 Case IV: VCB closing on LV side of WTSU transformer under inductive load ................ 82
4.4.5 Case V: VCB opening on HV side of WTSU transformer under no load .......................... 83
4.4.6 Case VI: VCB opening on HV side of WTSU transformer under inductive load .............. 85
4.4.7 Case VII: VCB closing on HV side of WTSU transformer under no load ......................... 86
4.4.8 Case VIII: VCB closing on HV side of WTSU transformer under inductive load ............. 87
vii
4.5 Summary .................................................................................................................................... 88
Chapter 5 Discussion ............................................................................................................................ 89
5.1 Investigation of VCB initiated transients on WTSU transformers ............................................. 89
5.2 Comparison of proposed VCB model with existing VCB model ............................................... 91
5.3 Comparison of results with switching transient analysis using power frequency transformer
model ................................................................................................................................................ 93
5.4 Problem of initial voltage spike and synchronized three-phase VCB model ............................. 94
5.5 WTSU Transformer model Validation ....................................................................................... 95
5.6 Summary .................................................................................................................................... 97
Chapter 6 Conclusions and Future Work ............................................................................................. 98
6.1 Conclusions ................................................................................................................................ 98
6.2 Future Work ............................................................................................................................... 99
6.2.1 Simulation and investigation of VCB initiated transients on whole wind farm .................. 99
6.2.2 High frequency DFIG model studies ................................................................................... 99
6.2.3 High frequency harmonics in the wind farm ....................................................................... 99
6.2.4 Measurement setup for admittance matrix of transformer ................................................ 100
Bibliography ....................................................................................................................................... 101
viii
List of Figures
Figure 1.1: Charles Brush's windmill [1] ............................................................................................... 3
Figure 1.2: Ontario supply mix 2013 and 2015 [4] ................................................................................ 4
Figure 1.3: Schematic representation of Type I wind generator ............................................................ 6
Figure 1.4: Schematic representation of Type II wind generator ........................................................... 7
Figure 1.5 Schematic representation of Type III wind generator .......................................................... 7
Figure 1.6: Schematic representation of Type IV wind generator ......................................................... 8
Figure 1.7: Location of WTSU transformer ........................................................................................... 9
Figure 1.8: Resonating frequencies created by harmonics [34] ........................................................... 10
Figure 1.9: The phenomena of restriking and TRV across VCB ......................................................... 11
Figure 1.10: Resonating frequencies created by harmonics transients ................................................ 12
Figure 2.1: Test circuit showing switching off of a motor with a circuit breaker ................................ 18
Figure 2.2: Reignition phenomenon in circuit breakers [33] ............................................................... 18
Figure 2.3: Description of multiple reignitions process [40] ............................................................... 19
Figure 2.4: Voltage and current waveforms across a breaker [33] ...................................................... 22
Figure 2.5: Frequency brackets and range in which transients propagate [43] .................................... 23
Figure 2.6: Example showing impedance vs frequency response ........................................................ 26
Figure 3.1: Test circuit used to simulate restrike phenomena in PSCAD/EMTDC ............................. 33
Figure 3.2: Black Box restrike module ................................................................................................ 34
Figure 3.3: Flow chart of restrike phenomenon in PSCAD/EMTDC .................................................. 35
Figure 3.4 Current across the VCB during phenomenon of restrike .................................................... 35
Figure 3.5: Zoomed in view of current across the VCB during phenomenon of restrike .................... 36
Figure 3.6: Bode plot showing impedance sweep of the test circuit during restrike mode.................. 36
Figure 3.7: Source voltage and load voltage of the test circuit during restrike .................................... 37
Figure 3.8: Zoomed view of source voltage and load voltage ............................................................. 37
Figure 3.9: Voltage across the VCB .................................................................................................... 37
Figure 3.10: Comparison of VCB voltage, load voltage, source voltage and VCB current during
restrike period ...................................................................................................................................... 38
Figure 3.11: Test circuit to demonstrate the black box VCB model in PSCAD/EMTDC ................... 39
Figure 3.12: Frequency scan of VCB circuit during the opening operation ........................................ 41
Figure 3.13: Opening operation of the test circuit during at 1.6 ms .................................................... 41
Figure 3.14: Zoomed in view of transient recovery voltage (Utrv) ..................................................... 42
ix
Figure 3.15: Opening operation of VCB at 1.6 ms ............................................................................... 43
Figure 3.16: Zoomed in view of transient recovery voltage (Utrv) ...................................................... 44
Figure 3.17: Zoomed view of first reignition ....................................................................................... 44
Figure 3.18: Phenomena of current chopping ...................................................................................... 45
Figure 3.19: Figure depicting 1.8 MHz component ............................................................................. 46
Figure 3.20: Voltage spikes during current chopping .......................................................................... 46
Figure 3.21: Successful Interruption of current .................................................................................... 47
Figure 3.22: Frequency scan of VCB circuit during the closing operation .......................................... 48
Figure 3.23: Closing operation of VCB at 4.7 ms ................................................................................ 49
Figure 3.24: Zoomed view of breaker current ...................................................................................... 49
Figure 3.25: Effect of prestrikes during the closing operation of VCB ................................................ 50
Figure 3.26: Zoomed view of breaker current ...................................................................................... 50
Figure 3.27: Zoomed version of Figure 3.25 ........................................................................................ 51
Figure 3.28: Opening of VCB at 19 ms ................................................................................................ 52
Figure 3.29: Zoomed view of TRV ...................................................................................................... 52
Figure 3.30: Zoomed view of Figure 3.29 ............................................................................................ 53
Figure 3.31:ABB XLPE cable modelled in PSCAD/EMTDC ............................................................. 55
Figure 3.32: Cable specified by PSCAD/EMTDC Frequency dependent phase model ....................... 55
Figure 3.33: N-Terminal transformer model ........................................................................................ 59
Figure 3.34: Admittance matrix measurements on the HV and LV side of the transformer ................ 59
Figure 3.35: Actual WTSU Transformer simulated in PSCAD/EMTDC ............................................ 59
Figure 3.36: Complete high frequency black box modeling technique of the WTSU transformer ...... 60
Figure 3.37: Network realization of admittance matrix in PSCAD/EMTDC ...................................... 65
Figure 3.38: Experimental setup to measure Y31 of the admittance matrix ........................................ 65
Figure 3.39: Terminal response of transformer in the form of an admittance matrix .......................... 66
Figure 3.40: Measured and calculated values of admittance matrix of the transformer ....................... 67
Figure 3.41: Measured and calculated values of phases of admittance matrix of the transformer ....... 67
Figure 4.1: Type IV wind turbine synchronized with the grid ............................................................. 69
Figure 4.2: DFIG model ....................................................................................................................... 70
Figure 4.3: Configuration of black box VCB in PSCAD/EMTDC ...................................................... 72
Figure 4.4: Parameters of cable model in PSCAD/EMTDC ................................................................ 73
Figure 4.5: FDNE module and curve fitting options ............................................................................ 75
x
Figure 4.6: Collection grid used in the test bench ................................................................................ 75
Figure 4.7: An example depicting different time regimes of transient waveform ............................... 76
Figure 4.8: Voltage waveform on LV side of WTSU transformer (not loaded) .................................. 78
Figure 4.9: Zoomed in view of voltage waveform at WTSU transformer LV terminal ...................... 78
Figure 4.10: Voltage waveform on LV side of WTSU transformer (loaded) ...................................... 80
Figure 4.11: Zoomed in view of voltage waveform at WTSU transformer LV terminal .................... 80
Figure 4.12: Voltage waveform on LV side of WTSU transformer (not loaded, closing) .................. 81
Figure 4.13: Voltage waveform on LV side of WTSU transformer (loaded, closing) ........................ 82
Figure 4.14: Post transient voltage oscillations for case IV ................................................................. 83
Figure 4.15: Voltage waveform on HV side of WTSU transformer (not loaded) ............................... 84
Figure 4.16: Zoomed view of voltage waveform for case V ............................................................... 84
Figure 4.17: Voltage waveform for case VI ........................................................................................ 85
Figure 4.18: Zoomed view depicting transient period for case VI voltage waveform ......................... 86
Figure 4.19: Voltage waveform on HV side of WTSU transformer (not loaded, closing) .................. 86
Figure 4.20: Voltage waveform across WTSU transformer terminals for case VIII ........................... 87
Figure 4.21: Zoomed in voltage waveform depicting transient period ................................................ 88
Figure 5.1: Frequencies corresponding to different regimes of the transient period for case VI ......... 91
Figure 5.2: TRV and current of VCB [67] ........................................................................................... 92
Figure 5.3: Voltage waveform at a transformer terminal in Mireanue's wind farm system [33] ......... 93
Figure 5.4: Overvoltage during de-energization of LMF transformer by the vacuum breaker [68] .... 94
Figure 5.5: Voltage ratios from high voltage side to low voltage side ................................................ 95
Figure 5.6: Voltage ratios from high voltage to low voltage side ........................................................ 96
Figure 5.7: Comparison of voltage ratios for measured, calculated and simulated values .................. 97
xi
List of Tables
Table 1-1: Latest Wind Generators [13] ................................................................................................. 5
Table 2-1: Relationship Between Switching Device Performance and Frequency Interval [41] ......... 20
Table 2-2: Transformer Models for Different Frequency Intervals [41] .............................................. 21
Table 3-1: The parameters of equation (3.7) at different dielectric strengths ...................................... 32
Table 3-2: The constants C and D at different current quenching capability ....................................... 32
Table 3-3: Calculation depicting the four different layers of cable model in PSCAD/EMTDC .......... 56
Table 3-4: Properties of the cable material ........................................................................................... 56
Table 3-5: Matching the inductance and capacitance of the cable ....................................................... 57
Table 4-1: Properties of VCB used in the test bench ........................................................................... 72
Table 4-2: Cable model specifications ................................................................................................. 74
Table 4-3: WTSU transformer parameters for FDNE module in PSCAD/EMTDC ............................ 75
Table 4-4: Quantitative comparison of test case I ................................................................................ 79
Table 4-5: Quantitative comparison of test case II ............................................................................... 81
Table 4-6: Quantitative comparison of test case III ............................................................................. 81
Table 4-7: Quantitative comparison of test case IV ............................................................................. 83
Table 4-8: Quantitative comparison of test case IV ............................................................................. 84
Table 4-9: Quantitative comparison of test case VI ............................................................................. 85
Table 4-10: Quantitative comparison of test case VII .......................................................................... 87
Table 4-11: Quantitative comparison of test case VIII ......................................................................... 88
Table 5-1: Quantitative Comparison Results of Switching Transient Study ........................................ 89
Table 5-2: Comparison of Similar Test Cases from Mireaneu [33] and Current Work ....................... 93
xii
Nomenclature
LTEP Long Term Energy Planning
WTSU Wind Turbine Step Up Transformer
VCB Vacuum Circuit Breaker
DFIG Doubly Fed Induction Generator
TOV Transient Overvoltage
TRV Transient recovery Voltage
1
Chapter 1
Introduction
Power systems have undergone profound changes over the past five decades. Energy producers are
looking at alternatives of traditional thermal plants that use fossil fuels in renewal energy sources,
such as wind and solar. In fact, a serious commitment to reduce carbon dioxide emissions, together
with the desire to avoid fossil fuel, has resulted in tremendous growth of wind energy around the
world. In Canada, every province is adopting wind power as a potential source of energy to
supplement its energy grid. The current wind power generation capacity in Canada is about 8517
MW, which accounts for 3.17% of the country’s total electricity demand [1]. Further, a strategy has
been outlined by Canada's association on wind energy that anticipates this form of energy reaching a
capacity of 56,000 MW by 2025 [1]. This will feed 20.5% of Canada's total electricity demand.
Some of the nuclear plants in Canada are in the process of being refurbished. As elsewhere in the
world, the inclination in Ontario is now towards the construction of wind energy systems as being
cost-competitive, stronger, and affordable. Ontario has invested $1.73 billion within the past five
years alone to install new wind farms with a capacity of 1,040 MW [2]. In 2013, a LTEP was released
in Ontario. The LTEP proposes the procurement of 300 MW of wind energy in 2015, while
identifying similar opportunities for 2016 [3]. As of December 2014, there were 69 wind farms
installed in the province of Ontario, with a total number of 1852 wind turbines. The province plans to
build 6,736 new wind turbines over the next 20 years, with a predicted contribution of 25% of
Ontario’s total generation capacity by 2035 [4].
Electrical utilities across North America are predicting a high dependability on wind power in the
near future [5]. However, these utilities have encountered serious challenges from the perspective of
power system transient studies when incorporating wind power into existing transmission and
distribution systems [6], [7]. A WTSU is installed with every turbine in a wind farm. The function of
this transformer is to ‘step up’ the output voltage level of the turbine generator from the generation
system rated voltage to the voltage level of the collector system, which is generally medium voltage.
Failures in these wind turbine step-up transformers have occurred at an alarming rate, leaving wind
farm operators and transformer manufacturers to identify the plausible causes of such failures.
Vacuum circuit breaker initiated high frequency steep front switching transients is expected to be
one of the reasons behind the wind turbine transformer failures. Wind turbines are typically switched
2
off several times a day due to extensive variations in wind speed, thus resulting in vast fluctuations in
power generated by the turbine unit. In such conditions, circuit breakers (commonly vacuum circuit
breakers) are used to isolate the unit from the collector grid. During the procedure of isolating the
wind turbine unit from the grid by VCB, transient overvoltages are produced due to switching
operation of VCB. These overvoltages are generated by ‘chopping’ the current, giving rise to
transient recovery voltage. The current chopping in synchronization with the transformer's inductance
and capacitance of the cable produces high di/dt and dV/dt. In the wind farms, each wind turbine is
equipped with WTSU transformer that is directly connected to vacuum circuit breaker through a
cable. Electrical systems with both long and short cables have shown the ability to produce transient
voltages at the transformer terminals containing high frequency oscillating waveforms. Despite the
fact that the magnitude of these transient overvoltages is less than the BIL rating of the transformer,
such an event can prompt high oscillatory voltages inside the transformer windings, resulting in
resonance thus causing transformer failures [8].
Standard power system deployment studies usually include reactive power requirement studies,
load flow, fault level, short circuit analysis, voltage ride-through capability, etc., but fail to provide
information about vacuum circuit breaker initiated steep front transient overvoltages experienced by
wind turbine step-up transformers [9]. This emphasizes the need to conduct switching transient
analysis studies for wind farms.
1.1 Background
1.1.1 Renewable energy systems: An overview
Renewable sources of energy have been an alternative for non-renewable sources of energy for the
past six decades. The benefits of renewable energy are that it is sustainable, pervasive, and generally
non-polluting. Moreover, solar cells and wind turbines do not utilize water to produce electricity,
giving these energy sources crucial advantages in dry areas such as the western and south western
portions of the United States [10]. In contrast, nuclear power plants and thermal electric plants use
huge quantities of water.
Despite their advantages, there are also some disadvantages associated with renewable energy. The
main ones are high initial cost, variability, and low density, as there is a need for a large captured area
and back-up power. Other disadvantages associated with renewable energy are brine from geothermal
energy, odor from biomass, avian and visual pollution issues related to wind farms, etc. [10].
Addit
due to
1.1.2
Wind
source
inven
The
centur
draini
water
Charl
[12].
Nor
wood
espec
centur
conne
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appea
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Evolution o
d power gene
e of energy
ntion of the ste
e 11th century
ries that follo
ing lakes at th
r for ranches a
es Brush's wi
rth American
d at saw mil
ially for light
ry saw the d
ected to the gr
crisis resulted
arance of addi
ding a large fa
ms, noise, and
of wind ene
ration is an e
for grinding
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y saw people
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he Rhine Riv
and farms and
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n pioneers use
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d lowered pro
ergy
evolving pro
g grain, pum
wind and wate
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Figure 1.1: C
ed windmills
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of small win
s the oil crisi
on of an inter
wer to existing3
newable energ
operty values
cess. In pre-i
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Charles Brush's
for grinding
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remote areas
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g generation s
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.
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and enablin
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[1].
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Figure 1
nd deploymen
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asily satisfied
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4
tario
ntional power
is a gradual in
013 to 8% in
an released b
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1.2: Ontario sup
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y have only
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s, etc., can be
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speed operati
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4
r source in th
ncrease in win
2015. Ontari
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demand for i
a slight im
ind power pla
efficiently ha
of Wind Fa
in the market
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roadly classifi
he Canadian
nd energy con
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f Energy in O
and 2015 [4]
ns in Ontario c
ployment act
increased win
mpact on grid
ants, such as
andled with p
arm Gener
. These differ
f connection
fied as [13]:
electrical ene
ntributions to
MW of powe
Ontario decla
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rs
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5
Permanent Magnet Synchronous Generators (PMSG)
Field Excited Synchronous Generators (FESG)
Doubly-Fed Induction Generators (DIFG)
An alternative way of classifying wind generators is by type of connection with the turbine,
whether gear connected or direct connected. Prior to 1990, manufacturers preferred gear connections,
as they are light weight and can convert relatively low wind speeds to the high rotational speeds
required by induction generators. Because of this ability, induction generators were quite small, and
the total weight of such systems was less compared to direct drive systems. However, the main
disadvantage of this approach is that it reduces the efficiency of the system. For this reason,
manufacturers today are more interested in direct drive generator systems, of which only synchronous
generators are currently available. Table 1-1 shows a comparison of the latest available wind
generators.
Table 1-1: Latest Wind Generators [13]
No. Generator type
Gearbox Manufacturer Power Rating
Turbine rotor speed
Generator voltage rating
Grid connection
type
Nacelle weight
Generator weight
1 FESG Yes DeWind 2MW 20 rpm 13.8 kV 4 62000 kg N/A
2 FESG Direct
drive
Enecron 4.5
MW
N/A N/A 2 N/A 220000 kg
3 IG Yes Vestas 850
kW
26 rpm 690 V 2 38000 kg N/A
4 IG Yes Vestas 2 MW 16.7 rpm 690 V 2 67000 kg N/A
5 IG Yes Vestas 3 MW N/A 1000 V 3 70000 kg N/A
6 DFIG Yes Gamesa 850
kW
25 rpm 690 V 3 33000 kg N/A
7 DFIG Yes DeWind 2 MW 20 rpm 690 V 3 62000 kg N/A
8 DFIG Yes Gamesa 2 MW 16 rpm 690 V 4 107000
kg
N/A
9 PMSG Direct
drive
Zephyros 1.5
MW
18 rpm 3000 V 4 N/A 47200 kg
10 PMSG Direct
drive
Vestas 3 MW N/A N/A 4 70000 kg N/A
11 PMSG Direct
drive
The Switch 3.8
MW
21 rpm 690 V 4 N/A 81000 kg
12 PMSG Yes The Switch 950
kW
N/A 690 V 4 N/A 3400 kg
Based
generators
Type I
control (2
regulated
transform
wind turb
this system
faster in
contrast, p
of the turb
wind, mec
Type I
more cont
Type II w
rotor indu
of a varia
achieved w
providing
constant d
on the type
s:
Wind Turbi
2-3%) of slip
to control p
mer is directly
bine remains f
m due to the
comparison
positive slip r
bine is almost
chanical inert
II Wind Tur
trol of slip (u
wind turbine g
uction generat
able resistor in
with the use o
g a path for t
during burstin
Gear Box
of grid inte
ine Generato
[14]. The ge
power. In thi
y connected to
fixed in conju
e creation of
to the speed
refers to the m
t linearly dep
tia of the syst
Figure 1.3: Sch
rbine Genera
up to 10%) an
generators hav
tors in a fash
n the rotor ci
of power elec
the current to
ng conditions
IG
6
egration inter
or: These are
enerators con
is type of wi
o the squirrel
unction with t
negative slip
d correspondi
motoring mod
pendent on the
em confines t
hematic repres
ator: These a
nd can consum
ve the turbine
hion similar to
ircuit of the m
ctronics and a
o flow betwe
s, the variable
Soft Start
6
rconnection,
fixed speed w
nsume reactiv
ind turbine c
l cage induct
the frequency
, which occu
ing to the fr
de. Under stea
e torque. Dur
the rate of cha
sentation of Ty
are variable s
me reactive po
e step-up trans
o type I turbi
machine, whi
a group of res
een the resist
e resistors pr
ter
Capacitor Ba
there are fo
wind turbine g
ve power and
configuration
tion generator
y of the grid.
urs when the
requency of t
ady state con
ring spasmodi
ange of outpu
ype I wind gene
speed wind tu
ower like typ
sformer direc
ines. The only
ich is not pre
sistors exterio
tors and the
rovide rapid c
ank
our classifica
generators tha
d the rotor bla
, the wind tu
r (SCIG). Th
Real power
shaft of the
the electrical
nditions, the o
ic variations
ut power (dP/
erator
urbine genera
e I wind turb
ctly connected
y difference i
sent in Type
or to the rotor
rotor [14]. T
control of the
Collector Fe
ations of win
at have limite
ades are pitch
urbine step-u
he speed of th
is generated i
turbine rotate
l grid [15]. I
operating spee
in the speed o
/dt) [16].
ators that hav
ine generator
d to the woun
is the presenc
I. This can b
and slip ring
To keep powe
e rotor curren
eeder
nd
ed
h-
up
he
in
es
In
ed
of
ve
rs.
nd
ce
be
gs,
er
nt.
Even
respon
Typ
turbin
power
gener
equip
only s
magn
there
power
during grid
nse.
pe III Wind
nes, but they
r control. Pa
rally referred
ped with var
simple resista
itude and pha
is back-back
r with the grid
GB
disturbances
Figure 1.4
d Turbine G
have more c
artial scale co
to as Type III
riable frequen
ance. A curre
ase of the rot
connection b
d.
Figure 1.5
Gear Box
s, the variab
4: Schematic re
Generator: Ty
control of slip
onverters are
I turbines and
ncy AC excita
ent-controlled
or current ser
between a grid
Schematic rep
IG
Soft
7
le resistors [
epresentation o
ype III wind
p (up to 50%
needed for
d are an upgra
ation of the r
d voltage sou
rves as an ext
d side convert
presentation of
t Starter
Capaci
[16] can infl
f Type II wind
turbine gene
%) and can p
this type of
ade to Type I
rotor circuit,
urce converter
ternal supply
rter and a roto
f Type III wind
itor Bank
fluence the m
d generator
erators are a
provide comp
wind turbine
II turbines. Ty
whereas Typ
r with adjusta
y to the rotor
or side conver
d generator
Collect
machine's dyn
also variable
prehensive rea
e [17]. DFIG
ype III turbin
pe II turbines
able control o
[14]. Additio
rter for excha
tor Feeder
namic
speed
active
Gs are
nes are
s have
of the
onally,
anging
Type I
Types II a
Reactive
turbines p
rotating m
turbine ro
generating
is similar
current co
1.3 Win
Every win
generator
level. The
rated from
grounding
transform
location o
V Wind Tur
and III, Type
power contro
provide an adj
machine via a
otates at optim
g less frequen
to wound rot
ontrol and hig
F
d Turbine
nd turbine in
turbines to t
ese transform
m 2 MVA -
g transformer
mer located at
of the WTSU
rbine Genera
IV also prov
ol is an addit
justable desig
a back-back f
mal speed. T
ncy than the e
tor synchrono
gh numbers of
Figure 1.6: Sch
Step-Up T
a wind plant
he voltage of
mers are locate
5 MVA. For
rs are located
the substation
transformer i
IG
8
ator: Now a
ides variable
tional feature
gn and operat
frequency con
The machine
electrical freq
ous machines
f poles genera
hematic represe
ransforme
is usually equ
f the collecto
ed at the bas
r grounding p
d all across a
n supplying p
in a wind farm
8
day, this is th
voltage contr
of Type IV
tion because t
nverter. To o
runs at slow
quency of the
as well as to
ally found in h
entation of Typ
ers
uipped with a
r system, wh
e of the wind
purposes (i.e.
wind farm. T
power to the e
m.
he most wide
rol, but provi
wind turbine
the grid is con
obtain AC ou
w turbine spe
grid [19]. Th
o conventiona
hydroelectric
pe IV wind gen
a WTSU that
hich is typical
d turbine (off
, mainly to p
This system
electrical grid
ely used wind
ides 100% co
es [18]. Furth
nnected to th
utput from the
ed as gearbo
his type of rot
al-type genera
c plants.
nerator
raises the ou
lly set at a m
ffshore wind f
provide neutr
is connected
d [20]. Figure
Collector Fee
d turbine. Lik
ntrol over slip
hermore, thes
he output of th
e machine, th
ox is removed
tating machin
ators with fiel
utput voltage o
medium voltag
farms) and ar
ral grounding
to the step-u
e 1.7 shows th
der
ke
p.
se
he
he
d,
ne
ld
of
ge
re
g),
up
he
Typ
the su
wind
1.4 P
Despi
task f
reason
a.
pically, conve
ubstantial num
turbine transf
Problems A
ite the prevale
for utility com
ns for the fail
High frequ
distribution
output of th
frequencies
frequency of
F
entional distri
mber of recen
former design
Associated
ence of WTS
mpanies, wind
lures in WTSU
uency harmo
transformer
he inverter f
caused by ha
f the grid and
Figure 1.7: Lo
ibution transf
nt wind turbin
n [21], [22].
d with Wind
SU transforme
d farm operat
U transforme
onics from c
cannot simpl
feeds the WT
armonics. On
d can create hi
9
cation of WTS
formers have
ne transforme
d Turbine S
er failures, id
tors, and deve
rs have been
converter sid
ly be used as
TSU transfor
ne of these h
igh voltage sp
SU transformer
been used as
er failures, th
Step-Up T
dentifying why
elopers of WT
identified as
de: As menti
s a wind turb
rmer [8]. Fig
harmonic com
pikes.
r
WTSU trans
here is a need
ransforme
y they occur
TSU transfor
follows:
ioned earlier
bine step-up t
gure 1.8 sho
mponents can
sformers. Ow
d for a more s
ers
has been a te
rmers [23]. Se
in this chap
transformer, a
ws the reson
match the n
wing to
sturdy
edious
everal
pter, a
as the
nating
natural
Giv
har
3rd,
wit
har
thre
pro
tran
the
b. Loa
con
tran
ligh
per
des
red
The
to f
loa
thro
Per
ven this scena
rmonics. Seco
5th, 7th, 13th
thin the wind
rmonics [8].
ee times high
oblems of par
nsformer failu
severe effect
ading cycle
nditions of W
nsformers. Fi
ht loading or
rspective, thes
signed with h
duce these loss
e second prob
full load. Due
d multiple tim
ough the tran
riodic variati
Figure 1.8: Re
ario, WTSU t
ondly, due to h, 17th, and u
dings and the
Moreover, th
her than norm
rtial discharg
ure. Therefor
ts of harmonic
of transform
WTSU trans
irstly, the cor
when the tran
se core losses
igh-grade ori
ses.
blem concern
e to variations
mes a day [8]
nsformer win
ons in the
1
esonating frequ
transformers s
the use of in
up to 23rd are
other metall
he harmonics
mal 60 Hz wav
e, dissolved
e, WTSU tra
cs.
mer: Due to
sformers are
re losses conti
nsformer is si
s should be k
iented electric
ns spasmodic
s in wind spee
. Sudden load
ndings and c
loading phen
10
uencies created
should be des
nverters, harm
e produced. E
lic structures
produce bur
veforms. Add
gasses, loss o
nsformers sh
variations in
e totally dif
inue to occur
itting idle. Fu
ept minimal
cal lamination
changes in lo
ed, a WTSU
d variations r
an lead to th
nomena can
d by harmonics
signed to with
monics with f
Enhanced stra
of the transf
rdens and tem
ditional tempe
of life of a t
hould be desig
n wind speed
fferent from
because of th
urthermore, fr
[8]. A core co
ns and a choi
oad, from ful
transformer c
result in varia
hermal stress
result in m
s [34]
hstand these h
frequencies o
ay and eddy
former are ca
mperatures th
erature increa
transformer, a
gned specific
d, the loaded
conventiona
he relatively l
rom a long-ter
onstruction th
ice of core flu
ll load to no l
can experienc
ations in the c
ses within th
mechanical bu
high frequenc
f a multiple o
current losse
aused by thes
hat are almo
ase can lead t
and eventuall
ally to counte
and unloade
al distributio
long periods o
rm economic
hat is speciall
ux density ca
load and agai
ce variations i
current flowin
he transforme
urdens on th
cy
of
es
se
ost
to
ly
er
ed
on
of
al
ly
an
in
in
ng
er.
he
11
transformer windings. It also effects the insulation and clamping structures, and adds to
loosening of the windings. Periodic temperature fluctuations are experienced by transformer
cooling systems as well. Oil absorbs more gasses during heating, and when the oil cools, it
releases the gasses, which results in the formation of bubbles. These bubbles create hot spots,
giving rise to partial discharge and leading to the eventual deterioration of the insulation.
c. Proper sizing of transformer: To handle the unique conditions inherent in wind power,
WTSU transformers should be properly sized. If they are not, the resulting dielectric burdens
and overheating will eventually deteriorate the insulation system [23]. Hydrogen is
predominantly generated within the transformer because of overheating and dielectric stresses.
Increasing the kVA rating of the transformer has been potentially identified as a temporary
solution to this problem, but it eventually adds to the losses.
d. VCB initiated steep fronted transients: Steep front transient overvoltages caused by
switching are another major concern [24]. The wind turbine unit can be switched off multiple
times a day due to extensive changes in wind speed and corresponding fluctuations in
generated power. To isolate the wind turbine from the grid, circuit breakers are used. The
switching operation of vacuum circuit breakers results in transient overvoltages because of the
extensive cable network and transformers used in wind farms [25]. These transient
overvoltages are produced by current chopping and result in high di/dt and dv/dt.
Figure 1.9: The phenomena of restriking and TRV across VCB
Although switching overvoltages caused by TRV have a magnitude lower than the basic
impulse level of the transformer, such overvoltages can prompt a large oscillatory voltage
within the windings and lead to failures [26]. IEEE standard C570.142 deals with this subject
adequately.
Main : Graphs
sec. 0.0156 0.0158 0.0160 0.0162 0.0164 0.0166 0.0168 0.0170 0.0172 0.0174
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
kV
Utrv(Transient Recovery... Ub1 Ub2
Fig
Com
that
1.5 Thes
The thesis
Fig
gure 1.9 show
mpared to har
t deteriorate t
sis Organi
s is organized
Chapter 1 p
configuratio
associated w
Chapter 2 p
this area. Re
VCBs, cabl
switching tr
transients c
components
presented.
Chapter 3
PSCAD/EM
simulating s
frequency b
PSCAD/EM
gure 1.10: Reso
ws transients
rmonics, swit
the insulation
zation
d as follows:
provides a re
on of wind far
with them are
provides a com
esearch that d
les, transform
ansients) is re
created by th
is also iden
deals with
MTDC. An a
statistical phe
black box m
MTDC to enab
1
onating frequen
s alleviating
tching transie
n of transform
eview of the
rms. As well,
reviewed.
mprehensive
deals with the
mers and ge
eviewed. Add
he interactio
ntified. Final
the modelin
adaptive high
enomena, the
model of an a
ble transient a
12
ncies created b
because of
ents create hig
mer windings.
evolution of
, wind turbine
overview of t
e modeling o
eneration sy
ditionally, res
n of switch
lly, a brief d
ng of VCBs
h frequency
high frequen
actual WTSU
analysis of win
by harmonics tr
switching V
gh frequency
f wind powe
e step-up tran
the literature
of power syst
ystems (for
search done o
hing devices
description o
s, cables, an
model of a
ncy (phase) m
U transforme
nd farm.
ransients
VCB in elect
oscillations w
er and explai
nsformers and
and the prior
tem compone
analyzing hi
on the analysi
and other p
f the potenti
nd WTSU t
a vacuum c
model of cab
er model are
trical system
with high dv/d
ins the typic
d the problem
r work done i
ents, especiall
igh frequenc
is of switchin
power system
ial problem
transformer i
circuit breake
les and a hig
e simulated i
ms.
dt
al
ms
in
ly
cy
ng
m
is
in
er
gh
in
13
Chapter 4 presents a detailed analysis and propagation of switching transients in a wind
turbine that is synchronized with the grid. Four different cases are defined, where
switching transients generated due to the opening and closing operation of VCBs on lower
and medium voltages are analyzed. The most severe and onerous conditions are observed,
depending on various factors.
Chapter 5 provides a discussion on the results obtained at the end of chapter 4. In chapter
5, the comparison of the proposed transient study in wind farm with prior research work is
presented.
Chapter 6 presents the thesis conclusion and suggests future work in the field of switching
transient studies in offshore wind parks.
14
Chapter 2
Literature Review
In this chapter, details of the fundamental concepts of TOV, with special emphasis on switching
transients, are provided in order to facilitate an understanding of the succeeding chapters. The
transients presented here are the type caused by switching operations of vacuum circuit breakers
(VCBs). A review of switching transients is followed by an evaluation of high-frequency transients
due to switching of a three-phase transformer with a vacuum circuit breaker. A thorough literature
review on transient overvoltage in cable systems and high frequency transients in large wind farms is
presented in the latter part of this chapter. Finally, a discussion of "IEEE C57.142: Guide for the
Occurrence and Mitigation of Switching Transients by Transformer, Switching Device and System
Interaction" concludes this chapter.
In transmission and distribution systems, inevitable conditions like network switching operations
generate transient overvoltages. A transient overvoltage results from the reaction of the electrical
circuit to sudden variations in an electrical network, such as switching operations or a fault. A
transient is a process in which a power system moves from a steady-state condition to a transient state
[30]. It is generally very short-lived, ranging from microseconds to milliseconds [37, 38].
2.1 Classification of Transient Overvoltage
2.1.1 Impulse transients
Lightening is a cause of impulsive transients and is associated with the discharge of a current that can
reach up to 200 kA. The impedance of the system seen by the lightening current limits the
overvoltage developed in this case. Such, overvoltage situations often cause faults in power systems
due to insulation failures, which in turn cause supply interruptions and voltage sags throughout the
electrical network.
2.1.2 Oscillatory transients
Switching transients in power systems are a source of oscillatory transients. Circuit breakers are used
to isolate a fault that generates such oscillatory transients. In order to carry out maintenance
operation, the switching of distribution feeders and capacitor banks that are used to provide reactive
power support, is also considered as additional source of oscillatory transients.
15
Circuit breaker initiated switching transients
A switching overvoltage or switching surge is generated due to the interaction of the inherent
elements (inductance, capacitance and resistance) associated with an electric network. When a current
flows through an inductance, it produces magnetic flux. Any effort to change the magnetic flux (i.e.,
the current) will be opposed by the inductance, which is manifested by the generation of a counter
EMF in the inductance in a direction that will keep the magnetic flux (and the current) constant.
Therefore, when a circuit breaker tries to interrupt a current, a voltage is developed by the system
inductance to oppose the change in current. The faster a switch tries to interrupt a current, the higher
the resulting switching surge voltage is.
Shunt capacitor switching transients
Shunt capacitors are used extensively in power transmission and distribution systems as a means of
supplying reactive power for voltage support. These capacitors are implemented in the system to
control the system voltage, increase the power transfer capability, reduce equipment loading, and
lower energy costs by improving the power factor of the system. Depending on the level of reactive
power support needed, switching of capacitor banks takes place. As the capacitor is defined by the
instantaneous rate of change of voltage, the voltage at the bus bar collapses during the energization of
a discharged capacitor. This results in oscillatory transient voltage, with a peak reaching up to 2 p.u.
A similar effect is observed during the switching off of a capacitor, which results in a restrike. A
restrike occurs when the recovery voltage of a breaker causes the dielectric strength of switching
contacts to break, re-establishing the current in the circuit. Under certain network conditions, the
switching transients of a capacitor can be magnified to higher values. This often occurs when
transients that originate from medium voltage move to a low-voltage electrical network, with power
factor correction capacitors present. The overvoltage associated with this phenomenon can reach a
peak value up to 4 times the corresponding power frequency voltage.
2.1.3 Travelling waves
The parameters of transmission lines and cables are distributed, as are of transformer and generator
windings. The characteristic impedance of a circuit with distributed parameters is its ability to support
traveling transient waves of voltage and current. The influence of the distributed parameters on the
propagation of TOV depends on the frequency content of the waves.
16
Current and voltage waves travel in both directions from the point of excitation or disturbance. The
ratio of the amplitudes of the voltage and the current waves on a transmission line or cable is called
the characteristic impedance Z0 of the line and for a lossless line is given by (2.1).
Z0= Ω (2.1)
where L and C are the distributed inductance and capacitance, respectively, of the line or cable.
Typical values of characteristic impedance vary between 300Ω and 500Ω for overhead lines, and
between 30Ω and 60Ω for cables.
The velocity of the propagation of the waves for a lossless line is given by (2.2) and depends on the
medium of propagation. It is near the speed of light (3*108 m/sec) for overhead lines, and between
one-half and two-thirds of this value for underground cables [2].
ν = m/sec (2.2)
Like all other waves, travelling waves initiated by disturbances in power systems also have classic
wave characteristics such as reflection and refraction.
Reflection and refraction of travelling waves
When voltage and current waves propagate in power lines or cables, there exists proportionality
between the two. The proportionality constant is the characteristic impedance of the line or the cable.
When a wave arrives at a point of discontinuity (which could be an open end, an underground cable
or transformer where the characteristic impedance changes), two new wave pairs are generated to
keep this proportionality. One is reflected back and is superimposed on the incident wave, while the
other is transmitted beyond the discontinuity. The amplitudes of the reflected and refracted waves are
such that the voltage-to-current proportionalities are preserved for each.
V2 =( )V1 (2.3)
V3 =( )V1 (2.4)
The magnitudes of reflected and refracted voltage waves at a junction point with characteristic
impedance waves Za and Zb on the incident side and refractive side, respectively, can be quantified as:
17
Here, V1 is the incident wave, V2 is the reflected wave, and V3 is the refracted (transmitted) wave.
is called the reflection coefficient and is called the refracted coefficient.
The reflected current (I2) and transmitted current (I3) are given by:
I2 = - (2.5)
I3= - (2.6)
These different types of transients discussed here are characterized by the following:
a. Rise time
b. Decay time
c. Peak values of overvoltage
d. Maximum current
e. Rate of rise of voltage
2.2 Vacuum Circuit Breaker initiated high frequency transients
About six decades ago, when the first generation of vacuum circuit breakers was still in use, research
was mainly focused on high chopping current levels of circuit breakers. The chopping of a current in
accordance with a transformer or motor circuit creates high frequency overvoltages in the form of
reignition and restrikes [26], [52]. An investigation into current chopping behaviors of VCBs showed
that the choice of contact material influences the interruption performance of a breaker around current
zero [14], and that the chopping current was deduced to vary from 3A to 8A [27], [15]. Current
chopping differs for a SF6 circuit breaker or VCB [28], [33]. Moreover, the probability of reignition
due to current chopping is statistically high and depends on the type of contact material [29].
Equation 2.7 [40] deduces the chopping current in VCB.
Ich= (×i×α×β) q (2.7)
Where, = 2×π×50 Hz; α = 6.2×10-16 sec; β = 14.28 and q= (1- β)-1 are the values as suggested in
IEEE 57.142, and i refers to the magnitude of power frequency current.
In the late 1980s, after determining the working of VCBs, the interruption of transformers [51] as
well as the switching off of motors [49], [55] were carried out in order to provide enough information
for determining overvoltages and insulation co-ordination levels. This work was followed by the
creation o
vacuum c
Figure
Figure 2.2
certain ci
transform
complicat
switching
recognize
of single-phas
ircuit breaker
Figure 2
2.1 illustrates
2 demonstrate
ircumstances,
mer connection
ted because o
g transients’
e most severe
se test circuit
r [56].
2.1: Test circuit
Figure 2.2: R
s the test circu
es the reignit
, results from
n, despite the
of mutual cou
circuit param
overvoltages
L
Supply
1
ts that could
t showing swit
Reignition phen
uit under con
ting transients
m a single-p
e fact that th
upling [54],
meters (e.g.,
[58].
L1
C1
18
simulate the
tching off of a m
nomenon in cir
sideration, wh
s produced b
phase transfo
he delta-conne
[57]. In dete
length of ca
C
restrike and
motor with a c
rcuit breakers [
hich shows th
because of thi
ormer can b
ected transfo
ermining the
able), bus ba
C2
Motor
reignition ph
circuit breaker
[33]
he switching
is phenomeno
be applied to
ormer phenom
most severe
ars are varie
L2
r
henomena in
off of a moto
on [33]. Unde
o a delta sta
menon is mor
conditions fo
ed in order t
a
or.
er
ar
re
or
to
The
transi
voltag
ability
netwo
mater
conten
The
the m
interru
levels
The
three
overv
As
the lo
can d
perfor
e dynamic si
ent studies w
ge, chopping
y. Estimation
ork was mad
rials used wer
nt showed a l
e arc voltage
moment of cur
upters, the ar
s in the range
e switching o
potential sou
voltage caused
shown in Fig
oad in the form
deteriorate or
rmance with f
imulation of
was introduce
g current, vo
n for expecte
de. Two cont
re Cr/Cu and
lower breakin
of the vacuu
rrent zero (du
rc becomes u
of 3-8 Amps
of inductive l
urces of over
d by virtual cu
Figure 2
gure 2.3, over
m of a motor
r eventually
frequency int
a vacuum ci
ed in ATP/E
ltage breakdo
ed transient o
act materials
Cr/Cu with
ng capacity.
um circuit bre
uring the extin
unstable befor
[38].
loads like mo
rvoltages: cho
urrent choppi
2.3: Description
rvoltages pro
or a transform
fail. Table
terval.
19
ircuit breaker
EMTP [35]. T
own characte
overvoltage f
s did the reig
additives of Z
eaker is indep
nction of the a
re zero durin
otors and un
opping overv
ing [39].
n of multiple re
duced in VCB
mer is expose
2-1 shows t
r in power s
The model s
eristics, high
for a specific
gnition and e
Zinc, Tin and
pendent of w
arc) gives ris
ng the switchi
nloaded transf
voltage, multi
eignitions proc
Bs are lower
ed to these tr
the relationsh
system simul
simulated cha
h frequency
c configuratio
extinction of
d Li2O [36]. C
wide current r
se to a TRV. I
ing of small
former circui
iple reignition
cess [40]
in magnitude
ransients, the
hip between
lation softwar
aracteristics o
current quen
on of an elec
arcs. The co
Cr/Cu and hi
range [37]. Id
In modern va
currents at cu
its with VCB
n overvoltage
e but very ste
insulation of
switching d
re for
of arc
nching
ctrical
ontact
igh Cr
deally,
acuum
urrent
Bs has
e, and
eep. If
f loads
device
20
Table 2-1: Relationship Between Switching Device Performance and Frequency Interval [41]
Circuit Breaker
Performance
1 Hz - 3kHz 3 kHz - 20 kHz 10 kHz - 3 MHz 3 MHz - 20 MHz
Closing
Mechanical Pole
Spread
Important Very important Negligible Negligible
Prestrike effect Negligible Important Important Very important
Opening
High current
interruption
Important for
interruption
capability studies
Important for
interruption
capability studies
Negligible Negligible
Chopping current Negligible Important for
interruption studies
of small inductive
currents
Very important Negligible
Reignition effect Negligible Important for
interruption studies
of small inductive
currents and
capacitive currents
Very important Very important
High frequency
current
interruption
Negligible Negligible Very important Very important
As the transients observed occur in the high frequency range, the selection of the transformer is very
important. Table 2-2 suggests different transformer models classified based on frequency range [41].
21
Table 2-2: Transformer Models for Different Frequency Intervals [41]
Transformers 1 Hz - 3kHz 3 kHz - 20 kHz 10 kHz - 3 MHz 3 MHz - 20
MHz
No Surge
transfer
With surge
transfer
Short circuit
impedance
Very important Very important Important for surge
transfer
Negligible
Saturation Very important Very important Negligible Negligible
Frequency
dependent
series losses
Very important Very important Negligible Negligible
Hysteresis and
iron losses
Only for resonance
studies
Very important Negligible Negligible
Capacitive
coupling
Negligible Very important Important for surge
transfer
Very important
2.3 Overvoltage Transients Experienced in Cable Systems
In an electrical system comprised of a switching device, cables and transformers, high frequency
transients from the switching device are alleviated by the capacitance of the cable and the inductance
of the transformer. Designers of power systems are mainly concerned with steady-state frequency
design (or at least up to several orders of harmonics, as required by standards) rather than high
frequency transients. To analyze the cable reflections, accurate modeling of cables is required to
model the wave propagation, skin effect etc., in the cable.
Simply representing the cable as a π-model does not serve the purpose. For example, the
semiconductor screens have a dominant role on the propagation characteristics at high frequencies
[42]. To model the cable in PSCAD/EMTDC or any other power system transient analyzing software,
data is us
resembles
frequency
conditions
Due to
should als
for mode
transients
a good ov
Figure
extensive
2.4 High
A wind f
(circuit br
high frequ
sed from cab
s a cable in a
y effects, and
s throughout
the sheath t
so be included
ling a cable
in a cable ar
verview of how
F
2.4 shows the
cable system
h Frequenc
farm has an
reakers). Rese
uency transien
le guides and
a real system.
d to choose
a large freque
that is presen
d when mode
in PSCAD/E
re given in [43
w transients t
Figure 2.4: Vol
e voltage and
ms [33].
cy Transie
extensive ele
earch has bee
nts in wind pa
2
d in electrica
. The idea is
an approach
ency spectrum
nt in an actu
eling a cable.
EMTDC. Som
3] and [44], w
travel in cable
tage and curren
d current acros
nts in Win
ectrical netw
en carried out
arks and to pr
22
al system des
to be able to
h for cable m
m [33].
ual cable, the
High frequen
me examples
which, along
es.
nt waveforms a
ss a breaker o
d Farms
work of cable
to analyze th
resent an anal
criptions to c
o simulate bo
modelling th
e high freque
ncy effects of
s of the prop
with their res
across a breake
of an industri
es, transforme
he generation
lysis as well a
create a mod
oth low frequ
hat accurately
ency coupling
f power cables
pagation of h
spective refer
er [33]
al system tha
ers, and swit
, propagation
as key results
del that closel
uency and hig
y reflects re
g phenomeno
s are importan
high frequenc
rences, provid
at makes use o
tching device
n and impact o
.
ly
gh
al
on
nt
cy
de
of
es
of
In
opera
grids
system
Conse
transi
in cab
system
The
freque
major
system
of dif
Figur
on the
high f
Tra
the st
transi
transm
propa
cable netwo
ations, causing
are composed
ms have low s
equently, mu
ent overvolta
ble grid (parti
m and the rela
e analysis of
ency modelin
r power syst
ms. The mode
fferent wind fa
Fig
e 2.5 implies
e lower frequ
frequencies.
ansformers co
tress of very
ent voltage in
mission syste
agation of ve
rks, multiple
g high freque
d of a vast am
surge impeda
ultiple prestrik
ages with larg
icularly wind
ated transient
high frequen
ng of major c
tem compone
els need to be
farm topologie
gure 2.5: Frequ
a relative ord
uency spectru
onnected at th
fast transient
n such system
ems at a hig
ry fast transi
e prestrikes
ncy steep-fro
mount of cable
ance compare
kes and reign
er time deriva
parks), it has
s during man
ncy switching
components r
ents include
e valid for hig
es has also be
uency brackets
dering, where
um (TRV osci
he medium-vo
s generated d
ms is much sho
gh-voltage lev
ients with a
23
and reignitio
onted transien
es of differen
d to overhead
nitions of sw
atives than ov
s become imp
oeuvres with
g transients in
responsible fo
cables, tran
gh frequency
een investigat
s and range in w
eby transient o
illations), wh
oltage level i
during breake
orter compare
vel. The tran
35-ns rise ti
ons are know
nt voltages an
nt lengths and
d lines in conv
witching appa
verhead transm
portant to cha
different swi
n wind parks
for high frequ
nsformers, cir
(i.e., 60 Hz t
ted [47].
which transient
oscillations d
hile cable refl
in wind park
er switching o
ed to the rise
nsformer exc
ime and a 1-
wn to occur
nd currents. W
d connecting p
ventional tran
aratuses with
mission lines
aracterize a co
itching appara
starts with th
uency switchi
rcuit breaker
to 10 MHz) [
ts propagate [4
due to system
lections occur
collection gr
operations. T
times of tran
citation with
-p.u magnitu
during swit
Wind farm col
points. These
nsmission sys
h cables can
s. With the inc
ollection grid
atuses [45].
he creation of
ing transients
rs, and gene
[46]. The infl
43]
components
r at relatively
rids are expos
he rise time o
nsients genera
VCBs show
ude. The inter
tching
llector
cable
stems.
cause
crease
cable
f high
s. The
ration
luence
occur
y very
sed to
of the
ated in
ws the
r turn
24
voltage among the windings exceeds the level obtained with a lightning impulse-shaped voltage
waveform of 4.4 p.u. During a switching scenario with delta-connected transformers, where the
winding is excited from both ends, the same 1-p.u./35-ns voltage step generates an inter turn voltage
that exceeds the 1-p.u. level, which is more than 2.5 times higher voltage stress than during a
lightning impulse test [45].
The voltage transients generated during breaker operations in cable systems in a wind park
collection grid can reach very low-rise times. The rise times of these transients can be almost 50 times
shorter than the rise time of a lightning pulse. Such transients can generate a very high voltage stress
on the internal transformers insulation [46].
A critical switching scenario for estimating internal voltages using verified models of different
types of transformers and wind turbine layouts (in order to account for typical wind turbine layouts
found in modern wind farms) shows that the magnitude of the voltage transients is higher than the
basic lightning impulse insulation level (BIL) [47]. Moreover, the rise time of the voltage surges is
much shorter than the rise time of the lightning pulse. The shortest rise time of 40ns is obtained in a
wind turbine layout where the wind turbine breaker is placed near the transformer. Due to very short
rise times of the transients, very high internal overvoltages are estimated in dry-type transformer
windings.
These internal overvoltages are much higher than overvoltages recorded for the basic lightning
impulse level. For a wind turbine layout where a breaker is placed in the bottom of a tower and a dry-
type transformer in a nacelle, the highest turn-to-turn voltage of about 1.5 pu is estimated. This is
almost 4 times higher turn-to-turn voltage then the voltage obtained during the BIL test. In a wind
turbine layout where a breaker is placed close to the transformer, the amplitude of the turn-to-turn
voltages reached 1.8pu due to lower stray capacitances and thus a shorter rise time of voltage strikes
[48].
2.5 Occurrence and mitigation of switching transients
The purpose of this IEEE guide (IEEE standard 57.142) is to provide a detailed description of the
transformer’s performance when impacted by oscillatory transients. These transients are typically
produced upon interactions of the electrical system, switching device (not mechanical switching
devices), transformer and load. The guide describes the operating conditions, which lead to the
production of switching oscillatory transients, eventually resulting in damage to a transformer
25
insulation system. The nature of the interaction and electrical characteristics of the above-mentioned
components is discussed in the guide, which also addresses several mitigation methods. The
document provides a specific guide to the modeling technique of major power system components
used to analyze switching transients in power systems.
The source and its corresponding transmission system is represented as a network of capacitances
and inductances. Since the transient frequencies are significantly higher than the system power
frequency, the dominant system parameters are the surge impedance or the capacitance of the cables
and lines. The short circuit inductive impedance is not an important parameter. As far as generation
systems are concerned, adaptive approximated models of different generators are used to simulate
switching transients.
The loads of concern are mainly transformers that are unloaded, lightly loaded and inductively
loaded. Non-linear loads (rectifier, variable speed motor drive, UPS system) may also be of concern,
depending upon the impedance presented at the terminals of the transformer's natural frequencies.
Severe voltages within the winding structure that produce stresses greater than the safety operation
limit of the transformer’s insulation are produced within the transformer, if the transient voltage
produced by system has a major oscillatory component at a frequency near to the natural frequency of
the transformer.
Transformers possess a frequency-dependent impedance characteristic, as shown in Figure 2.6.
Hence, the relationship between voltage across a transformer’s terminals and voltage produced within
the windings of a transformer non-linearly depends on the frequency content of the voltage applied
and the surge impedance of the transformer [49], [50]. Each individual transformer has a unique
design that corresponds to its impedance v/s frequency curve. Hence, creating an equivalent
frequency-dependent black box model of the original transformer is very important for the analysis of
switching transients [50].
According
characteri
D
C
C
B
In
R
2.6 Prob
Literature
network c
switching
frequency
have been
tests and h
farms cou
voltage tr
to conduc
switching
F
g to IEEE 57
istics:
Dielectric stren
Contact gap at
Current chopp
Breakdown vo
nterruption of
Repetitive reig
blem Ident
e review prese
conditions ca
g devices, wh
y TOV in win
n reported [36
had assemble
uld be the so
ansients caus
ct VCB initia
g overvoltages
Figure 2.6: Exa
7.142 standar
ngth between
current zero
ing magnitud
oltage (reignit
f high frequen
gnitions after
tification
ented in this
ause switchin
ich consist of
nd farms. WT
6], although t
ed all standard
ource of insu
ed by multipl
ated switching
s experienced
2
ample showing
rds, a switchi
contacts duri
during interru
de during inter
tion) after a cu
ncy inrush cur
interrupting h
chapter concl
ng overvoltag
f intense cabl
TSU transform
the failed tran
d requirement
ulation failure
le prestrikes a
g transient an
d by WTSU T
26
g impedance vs
ing device sh
ing closing
uption
rruption
urrent zero du
rrents followi
high frequenc
ludes that sw
ges with fast
le networking
mer insulation
nsformers had
ts [37]. The u
es in WTSU
and restrikes
nalysis studie
Transformers.
s frequency res
hould be able
uring interrup
ing reignition
cy inrush curr
witching devic
t rise times.
g. This increa
n failures cau
d previously p
use of cable n
transformer
of VCBs [39]
es for wind fa
sponse
e to simulate
ption
ns
rents
ces like VCB
Wind farms
ases the likel
used by switch
passed all qua
networks and
due to the fa
]. This empha
arms, to anal
e the followin
, under certai
use VCBs a
lihood for hig
hing transien
ality assuranc
VCBs in win
fast steep fron
asizes the nee
lyze the sever
ng
in
as
gh
nts
ce
nd
nt
ed
re
27
2.7 Research Objectives
As the unpredictable problem of transient overvoltage and unavoidable switching action of VCBs, it
is important to study fast switching transient overvoltage in wind farms. Despite the rising failure rate
of WTSU transformers due to stresses from fast switching transient overvoltage, there is very little
work done towards investigating and analyzing the switching transients experienced by WTSU. Due
to this reason, following research objectives are set for this thesis:
Developing a detailed user defined high frequency black box model of VCB in
PSCAD/EMTDC, proficiently simulating overvoltages on all the system components, taking
into account the statistical phenomena of VCB.
Developing a single core cable model based on the geometry of cable, insulating material
properties and incorporating a propagating wave frequency dependent phase model in
PSCAD\EMTDC.
Development of a sophisticated black box model of WTSU transformer using vector fitting
algorithm and rational function approximation technique, in PSCAD\EMTDC. Presentation
of an average model of DFIG concludes the simulation of power system components for
switching steep front transient analysis.
Simulating a test setup in PSCAD\EMTDC consisting of a Type-IV wind turbine
synchronized with a grid to analyze the most onerous transient scenarios experienced by
WTSU transformers.
28
Chapter 3
High Frequency Models of Wind Power Components
This chapter outlines the techniques of high frequency modeling of power system components that
are responsible for propagation of switching initiated high frequency transients in a wind farm. These
components are the switching device VCB, cables and wind turbine step up (WTSU) transformer. A
detailed model of VCB that illustrates overvoltages not only on circuit VCB itself but also on the
system components, considering all the statistical properties of VCB is outlined. The cable model
based on the geometry, insulating material properties and type of connection with the electrical circuit
incorporating a propagating wave frequency dependent phase model is presented. Elaboration of a
sophisticated black box model using vector fitting algorithm and rational function approximation
technique, in broad frequency range (20 Hz to 20 MHz) of WTSU transformer concludes the chapter.
3.1 Modeling of Vacuum Circuit Breaker in PSCAD/EMTDC
VCB is capable of quenching high frequency currents. The current quenching capability in
synchronization with dialectic recovery characteristics result in high transient recovery voltage across
VCB contacts. This statistical behavior of VCB's conducting arc causes interruption of high
frequency current, eventually inducing numerous reignitions. Reignitions, depending on external
circuit, may lead to critical overvoltages along the adjoining power system components. An accurate
and complete model of a VCB in PSCAD is discussed in [31]. Following four criteria described in
[59], should be taken into consideration for VCB model in PSCAD/EMTDC to show the statistical
occurrence of reignitions:
VCB contact opening can start before the natural current zero crossing
First reignition occurs when high transient recovery voltage exceeds the withstand voltage of
the VCB
The phenomenon of reignition is followed by high frequency currents being superimposed on
current zeros
VCB model should have the ability to interrupt the high frequency current
29
For analyzing high frequency steep front transients in WTSU Transformer, a detailed high
frequency model of VCB is developed in PSCAD/EMTDC. The model is able to simulate following
statistical phenomena:
a. Arbitrary nature of arcing time, i.e. the time between arcing phenomena and current zero
b. Effective current interruption at high arcing times
c. Interruption debacles for lower arcing times
d. At high arcing times, no restrikes and reignitions occur
e. At low arcing times, single or multiple restrikes
f. Overvoltages due to current chopping
g. At lower closing times there are no pre-strikes.
h. At high closing times there are single or multiple restrikes
i. High frequency current quenching capability
3.1.1 Explanation of physical phenomena within a VCB
3.1.1.1 Current Chopping
During the opening operation of VCB, an arc is generated across the VCB contacts, as the current is
yet to reach a natural zero crossing. At small magnitudes of current, the generated arc is unbalanced
and terminates before the current zero crossing. Such event normally occurs at 6A and causes steep
front transients depending on electrical system under consideration. This phenomenon is defined as
current chopping.
Due to non-deterministic nature of chopping current, earlier researches have defined distinct load
current chopping levels for different contact materials [33]. According to [33] mean chopping current
Ich is estimated by (3.1) as:
Ich=(⨯i⨯α⨯β)q (3.1)
Where;
= 2⨯π⨯f Hz (3.2)
i = amplitude of power frequency current (3.3)
α = 6.2 ⨯ 10-16 sec (3.4)
β = 14.3 (3.5)
q=(1- β)-1 (3.6)
30
3.1.1.2 Cold gap breakdown
During the separation of VCB contacts, the withstand breakdown voltage of the contact gap changes
linearly with time. This process takes finite amount of time. An arc is generated across the contact
gap of the vacuum, when the transient recovery voltage of the vacuum gap surpasses the threshold
voltage of the VCB. The electrical circuit is closed again as the high frequency arc is reignited across
the contact gap. Thus cold gap breakdown depends on rate of rise of transient recovery voltage [33].
3.1.1.3 Voltage escalation and re-ignitions
Reignition takes place because voltage breakdown of the circuit VCB initiates a high frequency
oscillatory current as the arc conducts. The oscillatory frequency is generated because of stray
capacitance and stray inductance of VCB and the external circuit parameters. The high frequency
current interrupts the circuit, clamping the load side voltage to a higher value. Now, transient
recovery voltage across the VCB rises and goes beyond the withstand capability of the VCB, giving
rise to further breakdowns. This phenomenon is called voltage escalation, as every following voltage
breakdown will clamp the voltage to a higher voltage level. Voltage escalation is dependent on the
natural resonating frequencies and is a function of electrical path created by the external circuit [10].
A temporary breakdown of the buildup voltage across the vacuum gap, taking place during the first
quarter cycle is defined as reignition. Reignition generally takes place after the first current
interruption. However, a restrike happens after a quarter cycle that takes place due to switching of
capacitive circuits [60], [52].
3.1.1.4 Current quenching capability of VCB
High frequency arc generated across the contacts of the VCB has certain inertia of its own. This
inertia will succumb the interruption, when the arc goes through high frequency current zero.
Therefore, in a precise model of VCB, initial high frequency current zeros are not obstructed and
actual arc interruption takes place after these non-interrupted current zeros have passed. The current
quenching capability of VCB is a measured from first order derivative of high frequency current
flowing through the arc. The arc across the vacuum gap extinguishes after a fixed number of zero
current crossings have passed.
31
3.1.1.5 Pre-strikes
The prestrikes are observed once the vacuum gap of VCB closes from an open position. During the
opening operation of a circuit VCB, reignition and restrikes are observed. The high frequency
phenomenon is similar for both prestrikes and restrikes. The only difference is that escalations in
voltage will not occur in prestrikes as the vacuum gap is shrinking with time [33].
3.1.1.6 Finite arc resistance
The high frequency current flows through the arc right after the cold gap breakdown. However, a
reignition voltage is imposed across the gap as this arc has finite resistance. This re-ignition voltage
depends on the rate at which the high frequency current rises and the impedance of external circuit
[33].
3.1.1.7 Probabilistic attribute of the VCB model
The VCB high frequency phenomenon is highly probabilistic and is derived from experimental
values. A sophisticated VCB model should accommodate the statistical nature of arcing time [33].
3.1.1.8 Hot gap breakdown
Hot gap voltage breakdown occurs after the arc across the contacts has extinguished. Surplus charge
carriers that endure on the surface of VCB contacts reduce the length of breakdown gap. These
surplus charges cause the breakdown of vacuum gap at lower voltage than expected [33].
3.1.2 Dielectric Strength Calculation
While modeling the dielectric strength of VCB, it is important to define voltage withstand capability
of galvanic contacts. In the proposed VCB model, cold and hot gap breakdown cumulatively define
the voltage withstand capability of VCB. VCB's contact distance derives the gap breakdown
characteristic. It is assumed that, the dielectric withstand capability of VCB is linearly dependent on
speed of switching operation [61]. Equation (3.7) represents the linear variation of dielectric strength:
V A t t B(3.7)
The parameters A and B at different dielectric strengths are listed in Table 3-1 [2].
32
Table 3-1: The parameters of equation (3.7) at different dielectric strengths
Dielectric Strength
A(V/Sec) B(V)
High 1.7E7 3.40E3 Medium 1.3E7 0.69E3 Low 0.47E6 0.69E3
Equation (3.7) represents the dielectric strength just after the contacts have separated, where the
constant A represents the opening speed. The same representation can be used for both opening and
closing the VCB as well as the closing time.
3.1.3 High Frequency Current Quenching Capability
Reignition occurs when the transient recovery voltage of the VCB contacts exceeds the dielectric
withstand capability of the VCB. Once reignition happens, high frequency current starts flowing
through the arc generated across the VCB contacts. VCB, with its current quenching ability can
interrupt this high frequency current. The successful interruption of high frequency current depends
on the first order derivative of high frequency current at natural zero crossing. For positive disruption
of the arc current, the rate of change of current at current zero should be less than the current
quenching capability of VCB [33]. The high frequency current quenching capability of a VCB is
represented in equation (3.8). The current quenching capability of the VCB is a function of speed at
contact opening.
C t t D(3.8)
The term represents the highest current derivative that the VCB can break at the current zero
crossing. The value of is summarized in Table 3-2.
Table 3-2: The constants C and D at different current quenching capability
Current Quenching Capability
C (A/s2)
D (A/s)
High -3.4E11 255E6 Medium 0.32E12 155E6
Low 1E12 190E6
3.1.4
This s
pre d
PSCA
consid
The
curren
strikin
follow
I
II
Fig
flowc
the V
Simulation
section descri
dominantly ha
AD/EMTDC
deration with
Figu
e electrical ci
nt interruption
ng in this ca
wing assumpt
I. The VC
restrike.
I. The res
specified
zero and
gure 3.3 show
chart supposes
VCB is close,
n of restrike
ibes the phen
appens in ca
to simulate t
a capacitive
ure 3.1: Test cir
rcuit is rated
n. An externa
apacitive circ
ions during si
CB can interr
strike occurs
d by the restr
d restrike).
ws the flowcha
s that the rest
there is a ph
e phenomen
omena of res
apacitive swit
the phenome
load.
rcuit used to sim
at 20 kV and
al black box
cuit controls
imulating the
rupt the high
every half
rike compone
at that simula
trike occurs ev
hase differenc
33
na of VCB in
trike in electr
tching circui
ena of restrik
mulate restrike
d is used to sh
model shown
a normal V
e above-menti
h frequency c
cycle of fun
ent (phase ang
ates the pheno
very half cyc
ce between c
n a capaciti
rical circuits w
its. A single-
ke. Figure 3.
e phenomena in
how the voltag
n in Figure 3
VCB model in
ioned phenom
current at the
ndamental fre
gle between p
omena of restr
le at the insta
current and vo
ve circuit
with capacitiv
-phase test s
1 shows the
n PSCAD/EMT
ge escalation
.2 that is use
n PSCAD/EM
mena:
e first curren
equency. Th
phase angle b
rike. The pro
ant specified b
oltage. Restri
ve loads. Res
etup is creat
test circuit
TDC
s during capa
ed to model th
MTDC. Ther
nt zero after
he restrike tim
between the cu
ogram shown
by the Tstrike. W
ike instant de
strikes
ted in
under
acitive
he re-
re are
every
me is
urrent
in the
When
ecides
34
whether the voltage is suppressed or escalated. For a capacitive current interruption, the worst
scenario is restrike at 180 degree after current zero (when Tstrike = 1/(2*60) = 0.008333s).
Figure 3.2: Black Box restrike module
Here flag is used to show whether the current is interrupted or not. Brk is the control signal of an
ideal VCB. Ibrk show the VCB current. Tstart is the time to start the restrike simulation, it should not be
confused with the instant of the current zero crossing or restrike. Tstrike is the interval of the first
current zero and the first restrike. Clock is the timer to determine if the restrike should occurs.
In the simulation, the restriking phenomenon starts at 0.05 seconds, and the angle between the
current zero and restrike is kept 180 degrees. The following plots are presented to observe the
restriking phenomena:
Current across the VCB
Voltage of the source
Voltage of the source
Voltage across the VCB
As stated earlier the restriking phenomenon starts at 0.05 seconds. The inductance of the source
and load capacitance resonates during the period of restrike to create a pre-dominant frequency
component, to which restrike occurs. The source inductance (L=0.001 H) and capacitance(C=80uF)
produce a resonating frequency (f1) of 558 Hz.
f1 = ∗ ∗ ∗
= 558.5 Hz (3.9)
This component of frequency can be seen as the restriking current in Figure 3.6. Impedance sweep
or the frequency scan of the circuit shows that there is a huge peak at 558.5 Hz and this frequency in
the current and the voltage during the period of the restrike.
Ibrk BrkBlack Box
Restrike
35
Figure 3.3: Flow chart of restrike phenomenon in PSCAD/EMTDC
Figure 3.4 Current across the VCB during phenomenon of restrike
Main : Graphs
Sec. 0.000 0.020 0.040 0.060 0.080 0.100 0.120
-80
-60
-40
-20
0
20
40
60
Curr
ent
in k
A
Breaker Current
36
Figure 3.5: Zoomed in view of current across the VCB during phenomenon of restrike
Figure 3.6: Bode plot showing impedance sweep of the test circuit during restrike mode
The load voltage, source voltage and VCB voltage experience similar overvoltages as the VCB
current during the period of restrike. Figure 3.7 and 3.8 show the relationship between the load
voltage and the source voltage. Source voltage gets clamped with the load voltage during the period
of restrike. In a purely capacitive circuit, as the one we have in the test system, if the restrike occurs at
1800 after current zero, the voltage escalations are 3,5,7,9...times the source voltage after every
restrike.
Main : Graphs
Sec. 0.000 0.020 0.040 0.060 0.080 0.100 0.120
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
Curr
ent
in k
A
Breaker Current
10-6
10-4
10-2
100
102
104
106
10-6
10-4
10-2
100
102
104
X: 558.5Y: 234.2
Zer
o S
eque
nce
Impe
danc
e in
ohm
s
Frequency in Hz
Frequency Scan of test circuit for simulating restrike phenomena in Capactive circuits
37
Figure 3.7: Source voltage and load voltage of the test circuit during restrike
Figure 3.8: Zoomed view of source voltage and load voltage
As explained earlier, the escalating voltages are odd multiples of the nominal rated voltage. The
voltage across the VCB is shown in Figure 3.9.
Figure 3.9: Voltage across the VCB
Main : Graphs
Sec. 0.000 0.020 0.040 0.060 0.080 0.100 0.120
-300
-200
-100
0
100
200
300
Volta
ge in
kV
Source Voltage Load Voltage
Main : Graphs
Sec. 0.0850 0.0900 0.0950 0.1000 0.1050 0.1100 0.1150 0.1200
-300
-200
-100
0
100
200
300
Volta
ge in
kV
Source Voltage Load Voltage
Main : Graphs
x 0.000 0.020 0.040 0.060 0.080 0.100 0.120
-300
-200
-100
0
100
200
300 Breaker Voltage
38
Figure 3.10 shows a comparison of voltages and current across the VCB, source and load during the
period of restrike. During restrikes, as can be seen in Figure 3.10 the voltage across the VCB goes
zero and the high frequency current flows through the VCB.
Figure 3.10: Comparison of VCB voltage, load voltage, source voltage and VCB current during restrike period
3.1.5 VCB model in PSCAD/EMTDC
3.1.5.1 Test system for simulating VCB in PSCAD/EMTDC
The test circuit for simulating the statistical and probabilistic model of VCB is shown in Figure
3.11 [62], [33]. This diagram simulates a 3.46 kV single-phase electrical system representing a
transformer, which is connected to a VCB through a cable. To keep the test circuit simple the
transformer and cable are represented by their equivalent R, L and C network.
Comparison
Sec. 0.0720 0.0740 0.0760 0.0780 0.0800 0.0820 0.0840 0.0860 0.0880 0.0900
-50 -40 -30 -20 -10
0 10 20 30 40
Cur
rent
in
kAm
ps
Breaker Current
-200
-150
-100
-50
0
50
100
150
Vol
tage
in
kV
Source Voltage Load Voltage
-200
-150 -100
-50 0
50 100
150 200
Vol
tage
in
V
Breaker Voltage
The
cable
cable
Rl=1e
= 100
It is
of the
freque
occur
The
resona
gener
Figure 3
e supply side
connection t
connected to
e5 ohm and L
0 µ.
s important to
e test circuit
ency compon
rring during th
e first freque
ates at a fre
rated due to ex
3.11: Test circu
connected to
together. Ln=
o the load. Cl
Ll=120 mH ar
o determine t
t with the fr
nent of 60 H
he VCB opera
ency compone
equency of 4
xchange of en
f
uit to demonstr
o the vacuum
=5mH, Cn=10
l=10nF is the
e representing
the resonating
frequency sw
Hz is ignored,
ation.
ent is the na
4.57 kHz. Th
nergy between
fload = ∗ ∗ ∗
39
rate the black b
m VCB is repr
00 nF. Rc=2
e cable capac
g the load par
g frequencies
weeps obtaine
, as we are c
tural resonati
he voltage o
n load inducta
∗= 4.57 kHz
box VCB mode
resented by th
ohm and Lc=
itance and lo
rameters. Cs =
manually, to
ed during the
concerned wi
ing frequency
oscillations o
ance and load
z
el in PSCAD/E
he Ln and Cn
=4e-2 mH ar
oad capacitan
= 0.0001 µF,
o match the re
e VCB oper
ith high frequ
y of the load
observed at t
d capacitance
EMTDC
n of the busba
re representin
nce added tog
Ls = 50 nF a
esonating bra
ration. The p
uency compo
d. This comp
this frequenc
e.
(3
ar and
ng the
gether.
and Rs
anches
power
onents
ponent
cy are
3.10)
40
Second frequency component is observed during the closing operation of VCB. In this case, the
switching operation creates a step change in the voltage oscillations across the load terminals, as
prestrikes are observed. The magnitude of the oscillating frequency is dependent on Lk and Ll. As
both of these inductances are in parallel and Ll is larger of the two, Lk will govern the equivalent
inductance. The capacitance seen by equivalent circuit is Cl, hence the observed resonant frequency is
f1 = ∗ ∗ ∗
= 250 kHz (3.11)
Once a step change in voltage is applied across the contact gap, a new frequency component arises
during the opening operation of VCB. The resonating branch for this frequency component comprises
of Ls and Lk in parallel with Ll. Lk dominates equivalent inductance of the circuit. Additionally, the
equivalent capacitances comprises of Cs and Cl, which are in parallel with each other. The observed
frequency component is at the frequency of f2.
Ceq = ∗(3.12)
f2 = ∗ ∗ ∗
= 1.8 MHz (3.13)
The test circuit anticipates a final resonant frequency of 50 MHz across the VCB contact terminals.
This frequency is observed because of series resonance of Cs and Ls. The frequency has been
eliminated from the analysis as an acutely feeble time step is required to capture this component. It is
observed that the frequency component of 50 MHz damps within 2μs, which is another reason of
excluding this frequency component from the analysis.
3.1.5.2 Opening operation of VCB
Under the opening condition of VCB in Figure 3.12, the resonating frequencies appearing in the
voltage using impedance sweep are presented.
Since the high frequency current flowing through the arc is of interest, we need to determine the
excitation frequency associated with this current. The negative peak as opposed to positive peak is
observed around 250 kHz. This confirms the theoretical calculations shown in the previous section.
The time step of 0.001 µsec is not feeble enough to capture 50 MHz frequency and is not seen in the
frequency scan.
41
Figure 3.12: Frequency scan of VCB circuit during the opening operation
Figure 3.13 shows the opening operation of the test circuit using VCB. The opening of VCB
contacts takes place at 16 ms and four reigntions are observed. The post transient oscillations take
about 8ms to die and are observed across the load voltage.
Figure 3.13: Opening operation of the test circuit during at 1.6 ms
The zoomed in view of transient recovery voltage (Utrv), during the opening of VCB contacts
shows four reignitions. This phenomenon can be observed in Figure 3.14.
10-6
10-4
10-2
100
102
104
106
108
10-8
10-6
10-4
10-2
100
102
104
106
X: 2.608e+05Y: 1406
MagnitudeofSequenceIm
pedance(ohm)
FrequencyinHz
FrequencyScanoftestcircuitwithVCBduringopeningoperation
10-6
10-4
10-2
100
102
104
106
108
-100
-80
-60
-40
-20
0
20
40
60
80
100
MagnitudeofsequenceAngleindegrees
FrequencyinHz
FrequencyScanoftestcircuitwithVCBduringopeningoperation
Main : Graphs
sec. 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
-20.0 -15.0 -10.0 -5.0 0.0 5.0
10.0 15.0 20.0
kV
Utrv(Transient Recovery V... Ub1 Ub2
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
Ib(Current across the breaker)
-15.0
-10.0
-5.0
0.0
5.0
10.0
kV
V load(Voltage across the load)
42
Figure 3.15 shows the VCB current and load voltage for the zoomed in TRV across the VCB.
Figure 3.14 depicts the transient recovery voltage across the VCB (Utrv), current of the VCB (Ib),
voltage across the load (Vload) and Ub1 and Ub2 show the voltage withstand capability of the VCB,
as referred in equation (3.7). The physical opening of the contacts starts at 0.016 seconds. The first
criteria needed for multiple reignitions is accounted by the prompt jump observed in the withstand
voltage of the VCB. The separation of VCB contacts should start before the natural current zero. This
phenomenon is depicted in Figure 3.14 during the initial opening across the VCB contacts.
Figure 3.14: Zoomed in view of transient recovery voltage (Utrv)
The frequency components explained in the previous sections are revealed in Figure 3.15. In the
switching transient study, the prime motive is to recognize high frequency components, hence a
minor time step is chosen. This tiny time step eliminates power frequency component in the observed
Main : Graphs
sec. 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
-30
-20
-10
0
10
20
30
kV
Utrv(Transient Recovery... Ub1 Ub2
Main : Graphs
sec. 0.0156 0.0158 0.0160 0.0162 0.0164 0.0166 0.0168 0.0170 0.0172 0.0174
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
kV
Utrv(Transient Recovery... Ub1 Ub2
43
waveforms. A time step of 0.01 µsec is required to precisely capture the high frequency components.
The model is verified from the results obtained in [62], [33].
Figure 3.17 shows the zoomed view of first reignition in TRV across the VCB as elaborated in
Figure 3.16, with corresponding VCB current and voltage across the load terminals. The small
transient observed in the beginning of Figure 3.17, is because of the chopping current that takes place
at 3 Amps. Figure 3.18 shows the chopping of the current and responsive TRV across the VCB
during the current chopping.
Figure 3.15: Opening operation of VCB at 1.6 ms
Main : Graphs
sec. 0.0158 0.0160 0.0162 0.0164 0.0166 0.0168 0.0170
-25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0
10.0 15.0 20.0 25.0
kV
Utrv(Transient Recovery V... Ub1 Ub2
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
Ib(Current across the breaker)
-15.0 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
10.0
kV
V load(Voltage across the load)
44
Figure 3.16: Zoomed in view of transient recovery voltage (Utrv)
Figure 3.17: Zoomed view of first reignition
Main : Graphs
sec. 0.0156 0.0158 0.0160 0.0162 0.0164 0.0166 0.0168 0.0170 0.0172 0.0174
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
kV
Utrv(Transient Recovery... Ub1 Ub2
Main : Graphs
sec. 0.01632 0.01634 0.01636 0.01638 0.01640 0.01642 0.01644 0.01646 0.01648
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
kV
Utrv(Transient Recovery... Ub1 Ub2
Main : Graphs
sec. 0.01632 0.01634 0.01636 0.01638 0.01640 0.01642 0.01644 0.01646 0.01648
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
kV
Utrv(Transient Recovery V... Ub1 Ub2
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
Ib(Current across the breaker)
-15.0 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
10.0
kV
V load(Voltage across the load)
45
Figure 3.18: Phenomena of current chopping
Diminishing voltage spikes are observed in Figure 3.16 and Figure 3.17 (further zoomed in Figure
3.19). The frequency component that creates these spikes needs further explanation. The arc between
the VCB contacts extinguishes when a fixed number of high frequency current zeros have crossed.
Once the arc extinguishes, the TRV across the VCB starts to increase. The high frequency component
observed at the inception of this phenomenon is 1.8 MHz. As the arc extinguishes the rate of rise of
voltage is very high. The high rate of rise of voltage succumbs the 1.8 MHz component, resulting in
TRV across the breaker surpassing the withstand voltage of VCB, causing subsequent breakdowns.
This phenomenon is observed as narrow spikes in the voltage waveforms.
It is worth observing the phenomena of reignition. As can be seen during the start of the simulation,
the voltage across the VCB is compared to the withstand capability of the VCB. As the TRV across
the VCB surpasses the withstand capability, the reignition occurs. The transients stop when the TRV
across the VCB is less than the voltage withstand capability of the gap, as observed in the first section
of Figure 3.21.
Successful high frequency current interruption is observed in Figure 3.21, when the TRV does not
exceed dielectric withstand capability of VCB. The time step chosen in this demonstration is different
Main : Graphs
sec. 0.01624 0.01626 0.01628 0.01630 0.01632 0.01634 0.01636 0.01638 0.01640 0.01642
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
kV
Utrv(Transient Recover... Ub1 Ub2
-0.0010
0.0000
0.0010
0.0020
0.0030
0.0040
0.0050
0.0060
0.0070
kA
Ib(Current across the breaker)
46
from previous graphs. The final purpose of VCB is to disrupt the current that is accurately depicted in
this waveform.
Figure 3.19: Figure depicting 1.8 MHz component
Figure 3.20: Voltage spikes during current chopping
Main : Graphs
sec. 0.01632 0.01634 0.01636 0.01638 0.01640 0.01642 0.01644 0.01646 0.01648
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0 kV
Utrv(Transient Recovery... Ub1 Ub2
Main : Graphs
sec. 0.016440 0.016445 0.016450 0.016455 0.016460 0.016465 0.016470 0.016475 0.016480 0.016485
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
kV
Utrv(Transient Recovery... Ub1 Ub2
Main : Graphs
sec. 0.016485 0.016490 0.016495 0.016500 0.016505 0.016510 0.016515 0.016520 0.016525
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
kV
Utrv(Transient Recovery V... Ub1 Ub2
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
Ib(Current across the breaker)
-15.0 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
10.0
kV
V load(Voltage across the load)
47
Figure 3.21: Successful Interruption of current
3.1.5.3 Closing operation of VCB
Under the closing condition of VCB in Figure 3.22, the resonating frequencies appearing in the
voltage waveform are presented. The frequencies with 886 kHz and 2.6 MHz components are
observed.
Previous section is dedicated to the problem of restrikes and depicts the phenomena observed
during the opening operation of VCB. During the closing operation of VCB, the problem of prestrikes
is observed (Figure 3.23). The amount of prestrikes depends on cold gap withstand voltage of the
VCB and the speed with which contacts of VCB close. In a peculiar condition, it is observed that the
high frequency arc between the galvanic contacts of VCB conducts the power frequency before
contacts are physically closed. This phenomenon is dependent on the rate at which VCB contacts
close.
Main : Graphs
sec. 0.01655 0.01660 0.01665 0.01670 0.01675 0.01680 0.01685 0.01690 0.01695 0.01700
-25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0
10.0 15.0 20.0 25.0
kV
Utrv(Transient Recovery V... Ub1 Ub2
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
Ib(Current across the breaker)
-15.0 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
10.0
kV
V load(Voltage across the load)
48
Figure 3.22: Frequency scan of VCB circuit during the closing operation
The phenomenon where current quenching capability of VCB is unable to snap the power
frequency current at zero current crossing is referred as an ineffective interruption. It becomes very
difficult for VCB to obstruct the current at high frequency, once the arc across the VCB contacts has
attained its natural inertia. Due to inability of VCB to interrupt this current no further zero crossings
are observed. Under such condition, the external circuit interrupts the arc at natural current zero. This
phenomenon is observed in the three-phase system, where three different phases are involved and due
to insufficient interruptions, second pole operates before the first pole and successfully succumbs the
current. Even though the arc conducts for longer than expected, the high dielectric withstand
capability of VCB contacts will result in no further breakdown and the high frequency arc is
terminated.
Figure 3.25 shows the effect of pre-strikes. As the VCB contacts are approaching the actual closing
state, the voltage between the contacts rises and cross the gradually diminishing dielectric withstands
voltage of the gap. An arcing current establishes, as the gap breaks down before the actual closing
state is reached. This phenomenon is attributed to hot gap breakdown characteristic of VCB's
galvanic contacts. This arcing current results in first pre-strike. Subsequently, the high frequency
conducting arc again establishes, depending on external electrical circuit. Second prestrikes are
observed once the VCB interrupts the high frequency current at next current zero. As this process
repeats numerous prestrike are observed. Resulting multiple prestrikes ensure steep front voltage
transients. This phenomenon is observed in Figure 3.27.
10-6
10-4
10-2
100
102
104
106
108
10-8
10-6
10-4
10-2
100
102
104
106
X: 4612Y: 8.892e+04
MagnitudeofSeq
uen
ceIm
ped
ance(oh
m)
FrequencyinHz
FrequencyScanoftestcircuitwithVCBduringclosingoperation
10-6
10-4
10-2
100
102
104
106
108
-100
-80
-60
-40
-20
0
20
40
60
80
100
X: 2.407e+06Y: -87.22
MagnitudeofSeq
uen
ceAngle(degree)
FrequencyinHz
FrequencyScanoftestcircuitwithVCBduringclosingoperation
49
Figure 3.23: Closing operation of VCB at 4.7 ms
Figure 3.24: Zoomed view of breaker current
Main : Graphs
Sec. 0.0000 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140
-0.075 -0.050 -0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175
kA
Breaker Current (kA)
-1.0
0.0
1.0
2.0
3.0
4.0
kV
Transient Recovery Voltage (kV)
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
kV
Load Side Voltage (kV)
Main : Graphs
Sec. 0.0000 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140
-0.075
-0.050
-0.025
0.000
0.025
0.050
0.075
0.100
0.125
0.150
0.175
kA
Breaker Current (kA)
Main : Graphs
Sec. 0.0033 0.0035 0.0038 0.0040 0.0043 0.0045 0.0048 0.0050 0.0053 0.0055
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
kA
Breaker Current (kA)
50
Figure 3.25: Effect of prestrikes during the closing operation of VCB
Figure 3.26: Zoomed view of breaker current
Main : Graphs
Sec. 0.0034 0.0036 0.0038 0.0040 0.0042 0.0044 0.0046 0.0048 0.0050 0.0052 0.0054
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
kA
Breaker Current (kA)
-1.0
0.0
1.0
2.0
3.0
4.0
kV
Transient Recovery Voltage (kV)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
kV
Load Side Voltage (kV)
Main : Graphs
Sec. 0.0033 0.0035 0.0038 0.0040 0.0043 0.0045 0.0048 0.0050 0.0053 0.0055
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
kA
Breaker Current (kA)
Main : Graphs
Sec. 0.00400 0.00405 0.00410 0.00415 0.00420 0.00425 0.00430
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
kA
Breaker Current (kA)
51
Figure 3.27: Zoomed version of Figure 3.25
3.1.5.4 VCB in a Three Phase System
The VCB used in the test bench is a three phase VCB and the user needs to analyze the effects of
choosing distinct operating instant for each phase of three-phase system. Figure 3.28 depicts the
electrical circuit chosen to observe the effects of three-phase VCB. The loads and electrical
configuration of the three-phase circuit is similar to the single-phase test circuit chosen before.
The test case is opening the VCB at 19 ms. Each phase observe different number of reignitions. A
different electrical configuration is observed by each phase of three-phase VCB because of 1200 phase
difference. As the current chopping is different at each phase, the TRV across each one of the phases
will be different, creating unique number of restrikes. This phenomenon is observed in Figure 3.29
[33]. This observation corresponds to real case scenario, where each phase shows different number of
restrikes or prestrikes because of unique current chopping level and virtual current chopping.
VCB_Closing_Prestrikes
Sec. 0.00400 0.00405 0.00410 0.00415 0.00420 0.00425 0.00430
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
kA
Breaker Current (kA)
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
kV
Load Side Voltage (kV)
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
kV
T ransient Recovery Voltage (kV)
52
Figure 3.28: Opening of VCB at 19 ms
Figure 3.29: Zoomed view of TRV
ThreePhase_VCB_Opening
sec. 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 0.0400
-30
-20
-10
0
10
20
30 TRV (kV) TRV1 (kV) TRV2 (kV)
-20
-10
0
10
20
load side voltage (kV)
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
breaker current (kA) breaker current1 (kA) breaker current2 (kA)
VCB_ThreePhase_BreakerTRV
sec. 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 0.0400
-30
-20
-10
0
10
20
30 TRV (kV) TRV1 (kV) TRV2 (kV)
VCB_ThreePhase_BreakerTRV
sec. 0.0185 0.0190 0.0195 0.0200 0.0205 0.0210 0.0215 0.0220 0.0225 0.0230
-30
-20
-10
0
10
20
30 TRV (kV) TRV1 (kV) TRV2 (kV)
53
Figure 3.30: Zoomed view of Figure 3.29
3.2 Cable Modeling
This section illustrates high frequency modeling technique of a power cable in PSCAD/EMTDC.
Eventual goal of the proposed cable model is to replicate high frequency behavior of the real power
cable. The cable model presented here incorporates the high frequency phenomena of skin effect,
reflections, electromagnetic transient propagation, speed of propagation etc. The model developed is
employed to formulate a novel test bench to investigate VCB initiated high frequency transients in a
wind farm.
In steady state power system studies, the power cable is represented as an equivalent RLC electrical
network. Nevertheless, for switching transient studies, a frequency dependent model that incorporates
the distributed parameters of the cable and is able to replicate high frequency phenomena of reflective
transients, should be used.
PSCAD/EMTDC accommodates three alternatives to a power cable model:
ThreePhase_VCB_Opening
sec. 0.0180 0.0190 0.0200 0.0210 0.0220 0.0230 0.0240
-30
-20
-10
0
10
20
30 TRV (kV) TRV1 (kV) TRV2 (kV)
-20
-10
0
10
20
load side voltage (kV)
-0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200
kA
breaker current (kA) breaker current1 (kA) breaker current2 (kA)
54
Bergeron model
Bergeron is the most basic model of the power cable. Here, cable is modelled as subsequent
sections of R, L and C. This model is employed in standard power system studies, to precisely
represent electrical response of a cable to an excitation frequency.
Frequency dependent mode model
Mode model employs the constant transformation of internal matrices to represent the high
frequency phenomena in a cable. As a major disadvantage, this model fails to replicate the cable
behavior during ideal transposition of core conductors.
Frequency dependent phase model
This is the most sophisticated cable model in PSCAD\EMTDC. In this model, dependency of
distributed parameters is defined for a particular range of frequency. The rational transformation
matrix uses frequency dependence characteristics to replicate phenomena like skin effect, reflections
and EM wave propagation. This model is used in switching transient studies.
Series impedance matrix and shunt admittance matrix are the primary parameters of power cables
or transmission lines. Equation (3.1) and (3.2) represent impedance and admittance matrices.
Z() = R(w) + jL (3.14)
Y() = G(w) + jC (3.15)
Where G, R, C, L are shunt conductance, series resistance, shunt capacitance and series inductance
respectively. Impedance and admittance are both function of frequency.
In PSCAD/EMTDC, parameters of the cable simulated depend on the geometry and physical
attributes of the specific material used in cable. Structural configuration of the proposed cable model
is different from the real cable. This model does not account for the semiconductor screen of the
actual cable. The cable model asserts that the core of the cable is a consistent conductor in
comparison to the core conductor in actual cable, which is made up of different strands.
The cable representation on in PSCAD/EMTDC only requires the geometric parameters for the
conductors, sheaths and insulators. PSCAD/EMTDC does not take into account the core stranding,
inner and outer semiconductor screens and wire screen.
PSCAD/EMTDC fails to represent following features of the cable:
1) Str
2) Sem
3) Wi
The p
steps
1. Cal
2. Spe
3. Cal
3.2.1
Figur
phase
descri
presen
The
PSCA
randing of cor
miconductor
ire screen
presented sect
are followed
lculate the dif
ecify the phys
lculate the pe
Layers of c
e 3.31 shows
e cable has a
ibed earlier,
nt in the mod
Figure
e Figure 3.32
AD/EMTDC.
re
layers
tions are used
to simulate c
fferent layers
sical propertie
r unit length c
cable mode
s the ABB X
cross section
core strandin
el of cable in
Figure 3.
3.32: Cable sp
2 shows four
Here, r1 repr
d to obtain par
able in PSCA
of the cable m
es of the cabl
capacitance a
el in PSCAD
XLPE cable t
n 95 mm2 and
ng, inner &
PSCAD/EM
31:ABB XLPE
pecified by PSC
layers of cab
resents the rad
55
rameters of c
AD/EMTDC:
model in PSC
e material use
and inductanc
D/EMTDC
that has been
d is designed
outer semico
MTDC, some la
E cable modell
CAD/EMTDC
ble that have
dius of the co
cable required
CAD/EMTDC
ed.
ce of the cable
n modeled in
to operate at
onductor scre
ayers should
led in PSCAD/
C Frequency de
to be specif
onductor. r2 c
d by PSCAD/
C.
e.
PSCAD/EM
a rated volta
eens and wir
be grouped to
/EMTDC
ependent phase
fied while rep
can be obtaine
/EMTDC and
MTDC. The s
age of 33.3 kV
re screens ar
ogether.
model
presenting cab
ed from the su
d three
ingle-
V. As
re not
ble in
um of
56
r1, main insulation thickness and outer & inner semiconductor thickness. r3 is obtained from radius r2
and radius of cross section of the screen. The outermost radius of cable is r4. Table 3-3 shows the
calculations for the four different layers of cable model in PSCAD/EMTDC.
Table 3-3: Calculation depicting the four different layers of cable model in PSCAD/EMTDC
Radius
Calculation
Value
r1
= .
= 5.6 mm
5.6 mm
r2
r2 = r1 + main insulation thickness + outer & inner semiconductor screen thickness
r2 = 5.6 mm + 5.5 mm + 0.5 mm + 1 mm = 12.6 mm
12. 6 mm
r3
r3 = A /π r
where As is the area of cross section of screen
13.26 mm
r4
= = 16 mm
16 mm
3.2.2 Physical properties of the cable materials used
The cable model not only requires the thickness of layers but also the physical properties of the
material of the layers. The approximated values used in the cable model in PSCAD/EMTDC are
given in the Table 3-4.
Table 3-4: Properties of the cable material
Cable material properties
Resistivity [Ω.m] Copper 1.7 × 10-8
Aluminum 2.82 × 10-8
Lead 1.9 × 10-7
Relative Permittivity XLPE 2.3
Permittivity [F\m] Vacuum 8.854 × 10-12
3.2.3 Matching the capacitance and inductance of the cable
Calculation of per unit inductance and capacitance of the cable is presented the Table 3-5.
57
Table 3-5: Matching the inductance and capacitance of the cable
Capacitance
Cper_unit= Ɛ Ɛ
=
. .
. / . = 217.56 pF/m
(3.16)
Inductance
Lper_unit= × µ0 × µr × loge(Routerinsulation/Rinnerinsulation) = 160.5 nH/m
(3.17)
Surge Impedance
Z0 = = 27.14 Ω
(3.18)
Wave travelling
speed
v = √
= 179.3 m/µsec
(3.19)
The four parameters presented above have been matched to the actual cable. Capacitance,
Inductance, surge impedance and wave travelling speed calculated are the within the 10% error range.
The expression that describes the inductance in (eq. 3.17) does not take into account the self-
inductance of the conductor, as this term is negligible at higher frequencies. This is because the skin
effect confines the current to external surface of the conductor. At high frequencies, the inductance
has a lower value, which is translated into lower characteristic impedance and a higher speed of
propagation.
3.3 Modeling of WTSU Transformer
Several resonance points due to inductive and capacitive effects from the windings, tank and core
characterize the high-frequency behavior of transformers. Overvoltage studies like switching transient
overvoltage study, resonant and transfer overvoltage study should incorporate the frequency
dependent behavior of the transformer. This section of the chapter outlines a procedure for
development of a high frequency black box model of an actual transformer, for the suggested
overvoltage studies. Specific modeling procedures used to obtain this model are presented in the
following sections.
58
This black box model is valid for a frequency range of 20 Hz to 20 MHz. The proposed model
incorporates the experimentally determined frequency dependent admittance matrix. The measured
admittance matrix is first approximated by means of rational function approximation and then fitted
via a vector fitting algorithm. Vector fitting is used to approximate the rational function of measured
admittance matrix, in form of partial fractions [63]. Finally, an experimentally calculated rational
function is formulated that is realized into a network of electrical entities (RLC) for time domain
simulations. The time domain simulations are carried out in PSCAD/EMTDC.
Specific measurements are carried along the transformer terminals to obtain the frequency
dependent admittance matrix. This admittance matrix characterizes low and high frequency behavior
of the transformer. The modeling procedure approximates the transformer's time invariant response as
a frequency dependent black box. Each block of the admittance matrix is a specific current-voltage
ratio. Obtaining all admittance values generates a 6*6 admittance matrix for the three phase
transformer. Vectorial curve fitting is then used to approximate the deduced admittance matrix for
rational function approximation.
3.3.1 Overview of Modeling Procedure
The three-phase transformer is considered an N-terminal device, as shown in Figure 3.33. The voltage
and currents are expressed in equation (3.20). Here Y(s) represents the admittance matrix and I(s) and
V(s) represent the current and the voltage vectors, respectively. Expanded vector formulation, voltage
and current vectors follow in equation (3.21).
I(s) =Y(s)*V(s) (3.20)
IIIIII
=
Y Y Y Y Y YY Y Y Y Y YYYYY
YYYY
Y Y Y YY Y Y Y (3.21)
As
produ
Simila
transf
the W
As
is to b
1
i
j
n
Vi- +Ii
Ij
can be seen i
uces an ith col
arly, the oth
former. Figure
WTSU transfor
VH1- + 1
2
3
HV S
Measu
Figure 3.
shown in Figu
e commissione
Transform
F
in Figure 3.33
lumn of Y(s)
her five colu
e 3.34 shows
rmer.
Side
urement on HV
.34: Admittanc
ure 3.35 the adm
ed in a wind fa
Figure 3.35: A
er
Figure 3.33: N
3, applying a
), where Yji c
umns can be
the measurem
4
5
VL4
VL5
VL6
LV Side
Side
ce matrix meas
mittance matri
arm.
Actual WTSU T
59
-Terminal tran
voltage of V
can be determ
determined
ment of admi
4
5
6
1
2
3
VH1
VH2
VH3
urements on th
x measuremen
Transformer sim
nsformer model
Viand zero vol
mined by find
for the thre
ittances on th
2
3
HV Side
Mea
he HV and LV
nts were perfor
mulated in PSC
l
ltage to the re
ding the ratio
ee-phase win
he low and hig
LV Side
asurement on L
side of the tra
rmed on a WT
CAD/EMTDC
emaining term
o between Ij
nd turbine st
gh voltage sid
- +4
6
VL4
LV Side
5
ansformer
SU Transform
C
minals
to Vi.
tep-up
des of
mer that
Once th
model of
approxim
transfer fu
WTSU tra
Fi
The fol
3.3.2 Rat
This secti
rational f
measured
approxim
iteration.
Equatio
data to a r
In order
with the
unknown.
mathemat
technique
technique
he admittance
the transform
ation, the rea
unctions. Figu
ansformer.
gure 3.36: Com
llowing sectio
tional appro
ion outlines
function app
admittance
ation of mor
The applicab
on 3.22 show
ratio of polyn
r to convert a
denominator
. However, t
tical problem
e is valid an
e is desired by
e matrix is ob
mer is realized
alized model
ure 3.36 show
mplete high fre
ons describe e
oximation o
rational func
proximation t
matrix in a
re than one
ility of this m
ws the approxi
nomials.
f(s) =
a nonlinear eq
r. The equati
this techniqu
m, as distinct
nd applicable
y rational fun
6
tained throug
d in PSCAD/
is validated
ws the compl
equency black b
each step of W
of frequency
ction approxim
technique us
broad frequ
frequency re
method is high
imation of or
quation to a li
ion considere
ue generates
powers of s
only for lo
nction approx
60
gh the measur
/EMTDC thro
by comparin
ete high freq
box modeling
WTSU transfo
y response
mation of ad
sed in this m
uency range.
esponse. This
hly accepted f
rder N by fitt
near one, eith
ed here is o
an asymmet
are multipli
ow order app
ximation algo
rement and th
ough vector f
ng the measu
quency black
technique of th
ormer modelin
by vector f
dmittance ma
method cons
The present
s method is
for realizing t
ting a given
her side of eq
of type Ax=b
trically calib
ied with colu
proximations.
orithm. Prior
he high freque
fitting and rat
ured and calc
box modeling
he WTSU tran
ng procedure
fitting
atrix via vecto
sistently app
ted techniqu
based on Sa
transformer's
set of freque
quation should
b and the co
rated and no
umns of A. T
. A sturdie
research stud
ency black bo
tional functio
culated voltag
g procedure o
sformer
in details.
or fitting. Th
proximates th
ue is valid fo
anthana-Koern
responses.
ncy dependen
(3.22
d be multiplie
oefficients ar
on-conditione
Therefore, th
er linearizatio
dies and fittin
ox
on
ge
of
he
he
or
nr
nt
2)
ed
re
ed
his
on
ng
61
algorithms clearly suggest that vector fitting algorithm is effective for modeling transformer
responses. Vector fitting extracts the approximated rational function from the measured raw data in
form of additive partial fractions. This is accomplished by compensating initial set of poles with an
augmented set of poles, through an iterative pole relocation method. The iterative pole relocation
method uses least square approximation algorithm to approximate the higher order responses [64].
The initial poles should be chosen to complement the augmented problem and must be
logarithmically distributed over frequency range of interest. As the passive nature is more dominant
during higher frequency range, the initial poles should be complex conjugate pairs instead of real
quantities.
Equation 3.23 demonstrates rational function approximation that is considered to demonstrate the
vector fitting method.
f(s) = ∑ + d + s.e (3.23)
Here f(s) represents a matrix of numerous responses as frequency dependent transfer function.
Residues and poles are represented by cn and an, respectively. Both residues and poles are complex
conjugate pairs and their passivity should be kept in check, while approximating the higher order
responses. The aim of this section, is to represent the function f(s) in terms of the variables on the
right hand side. For this purpose, the unknowns of f(s) should be calculated. Once the unknowns are
computed, f(s) can be easily approximated in the frequency range of interest. Hence, the problem
should be linearized as one of the unknowns an, is in the denominator. Vector fitting algorithm
linearizes the problem of higher order rational functions by identifying the poles and residues
separately.
A close observation of equation (3.29) shows that zeros of σfitted(s) are similar to the poles of f(s).
Hence, the problem of realizing poles of fitted f(s) can be tackled by obtaining zeroes of linear
equation (3.24).
σ(s) = ∑č
ā + d + s.e (3.24)
The augmented problem thus produced can be rewritten as follows:
=
∑ā
.
∑ č
ā 1 (3.25)
62
To linearize the rational function obtained in equation 3.25, the second row of equation 3.25 is
multiplied by f(s) giving equation 3.26.
∑ā
. = ∑č
ā 1 f(s) (3.26)
(σf)fitted(s) = σfitted(s)×f(s) (3.27)
Equation 3.27 is a linear problem of the type Ax=b in the frequency range of interest with certain
unknowns in the solution vector x.
From equation 3.27, we have
f(s) = (3.28)
Both numerator and denominator of equation (3.28) have the same poles. The ratio in equation
(3.28) can be rewritten as single fraction instead of sum of partial fractions, as shown in equation
3.29.
f(s) = e ∏
∏ ž(3.29)
A close observation of equation (3.29) shows that zeros of σfitted(s) are similar to the poles of f(s).
Hence, the problem of realizing poles of fitted f(s) can be tackled by obtaining zeroes of linear
equation (3.24).
Now, to precisely fit the approximated rational function, residues of the function f(s) should be
recognized. In order to linearize this problem and solve the residues by substituting the unknowns cn,
d and e, the zeroes of σfitted(s) presented above are used in the original problem (3.24) as new poles.
Approximation of rational function is completed by recognizing residues and poles of function f(s).
The next step is fitting the approximated rational function via vector fitting algorithm. To understand
the vector fitting algorithm and its formulation, the reader is referred to [64].
3.3.3 Passivity enforcement on the fitted admittance matrix
The intention of the previous section is to obtain a rational function approximation of frequency
dependent admittance matrix via vector fitting algorithm. Once an approximated rational function of
admittance matrix is obtained, an equivalent RLC network of transformer is realized in
PSCAD/EMTDC. The time domain RLC network thus obtained is passively linear time invariant.
63
During the transient simulations this model should behave passively in nature. Furthermore, for a
particular input voltage, the developed model should only absorb real power.
Due to the non-passive nature, transient simulations incorporating user defined modules obtained
via rational function approximation may result in instability. It has been observed that a user defined
model that is already tested and verified for stability and passivity, can still exhibit non passivity once
the model interacts with adjacent power system components during time domain simulations. Hence,
the equivalent RLC network of transformer should be checked for passivity compliance within the
frequency range of interest. Once the non-passive nature is identified, it should be removed. The
method of extracting the non-passive behavior is defined as passivity enforcement.
Passivity across the rationally fitted admittance matrix is checked by analyzing the real part of
admittance. For the admittance to be passive, the real part and corresponding Eigen values should be
positive definite. If found non passive, the network is enforced to a correction so that a positive
definite network can be realized. To minimize the fitting error caused due to variation of actual data, a
lower order correction is chosen. It is observed that non passivity can be kept in check by getting an
accurate measurement of admittance matrix. The passivity criterion using positive definite
determination is elaborated below [65].
The equation (3.30) defined an admittance matrix in the frequency range of interest
I=Y v (3.30)
Here I and v represent currents and voltages. The real power observed by the system is
P=Re v*Y v =Re v*(G+jB)v= Re v*Gv (3.31)
A close observation of (3.31) shows that; if the eigen values of G are kept positive definite then the
real power will always remain positive. Here '*' refers to transpose and should not be confused with
multiplication. For detailed understanding of passivity enforcement, the reader is referred to [30].
3.3.4 Time domain implementation after passivity enforcement
The elementary concept to create a high frequency transformer model, is to obtain an equivalent RLC
network of transformer terminal response in form of admittance matrix within a particular frequency
range. The final step of complete transformer modeling is predicting the equivalent RLC network.
The equivalent electrical network is generated from the rational approximation of fitted admittance
matrix.
64
The expression Y shown in equation 3.32 is approximated rational function of the measured
admittance matrix on transformer terminals using vector fitting algorithm. The fitted admittance
matrix in form of a rational function is given in equation 3.32.
Yfitted(s)ij =∑ . (3.32)
Equation 3.33 depicts the branches from nodes of realized electrical network to the ground:
yii= ∑ (3.33)
Electrical branches between different nodes are given by:
yjj=-Yfitting(s)ij (3.34)
Here n depicts the size of the matrix. As it is a three phase transformer the value of n is 6. For the
purpose of illustrating the time domain implementation, consider a single branch of the RLC network
derived from complex and real poles:
y(s) = + + --- + ṙ ṝ
ȃ ȁ +
ṙ ṝ
ȃ ȁ +
ṙ ṝ
ȃ ȁ +
ṙ ṝ
ȃ ȁ + --- + d + s.e (3.35)
Figure 3.37 shows an electrical network of parallel branches derived from evaluation of equation 3.35.
where,
Ro = ; Co = e ; (3.36)
RL circuit represents the real pole as;
Lr= ; Rr = -( ) (3.37)
The complex conjugate pair is given by RLCG network:
Lc= ; Rc = 2Lc (Lc(ṙ1ȃ1+ ṝ2ȁ2)-ȃ1) (3.38)
Cc = ȃ ȁ ṙȁ ṝȃ ; Gc = -2LcGc(ṝȃ+ṙȁ) (3.39)
3.3.5
The m
with i
to me
The
transf
curren
the ca
termin
subse
Co
Fi
Final WTSU
measurement
in a frequency
asure Y31 of t
e experiment
former to me
nt is done wi
ables from the
nals are conn
quently, gene
F
rrRo
onstant term
igure 3.37: Net
U Transform
of admittanc
y range of 20
the admittanc
al setup conf
easure 36 ad
ith a sensitive
e output term
nected to the
erating corres
Figure 3.38: Ex
Co
s.e term
twork realizati
mer model i
e matrix for
0 Hz to 20 MH
e matrix.
figured, uses
dmittance blo
e current prob
inal of netwo
input port o
ponding adm
xperimental set
rrRr
Lr
65
on of admittan
in PSCAD/E
WTSU transf
Hz. Figure 3.
the network
ocks and 9 v
be. The trans
ork analyzer to
of the networ
mittance values
tup to measure
rr
…
Real
nce matrix in P
EMTDC
former is don
38 shows the
analyzer, cu
voltage transf
sformer termi
o the transfor
rk analyzer to
s.
Y31 of the adm
L
Cc
Pole
PSCAD/EMTD
ne by using a
e measuremen
urrent probe,
fer functions
inals are exci
rmer terminal
o measure cu
mittance matri
rr
rr
Rc
Lc
c G
…
c
DC
a network ana
nt setup confi
cables and W
. Measureme
ited by conne
ls. The transfo
urrent and vo
ix
rr
rr
c
…
Complex conjugate pol
alyzer
igured
WTSU
ent of
ecting
former
oltage,
le
66
Figure 3.39 depicts the high frequency response of transformer terminals in form of admittance
matrix. These characteristics are obtained via direct frequency sweep measurements with sampling
window of 1201 points. Passivity enforcement over the raw data accounts for the inaccuracies due to
noise and other factors. The authenticity of measured admittance matrix is validated by 6 set of
identical measurements.
Figure 3.39: Terminal response of transformer in the form of an admittance matrix
Frequency dependent network equivalent (FDNE) model is used to simulate WTSU Transformer in
PSCAD/EMTDC. FDNE creates a multi-port, frequency-dependent network equivalent from given
characteristics, such as impedance or admittance values in a wide frequency range. The admittance
data given as a function of frequency is approximated using rational functions and vector fitting
technique. Once the parameters are expressed as rational functions, an electromagnetic transient-type,
frequency-dependent network equivalent is constructed, consisting of admittances and current
sources. Following parameters are to be chosen to simulate the frequency dependent equivalent model
of WTSU Transformer:
Maximum fitting error
Maximum order of fitting
Steady state frequency
Weighting factor from minimum to steady state frequency
Weighting factor of steady state frequency
102
103
104
105
106
107
10-10
10-8
10-6
10-4
10-2
100
102
Ad
mit
tan
ce (
S)
Frequency(Hz)
Admittance values for Three Phase Transformer
67
Weighting factor of steady state frequency to maximum frequency
Figure 3.40 and Figure 3.41 show the magnitude and phase of each admittance block in the
admittance matrix. An order of 23 is chosen for approximation of the rational function. The iterative
loop runs 6 times and passivity enforcement over 1201 points generate an equivalent RLC time
domain network. The frequency range of interest is 20 Hz to 20 MHz. The low frequency segment
around 600 kHz exhibit a near perfect fit, however, a very high resolution approximation is not
observed at high frequencies.
Figure 3.40: Measured and calculated values of admittance matrix of the transformer
Figure 3.41: Measured and calculated values of phases of admittance matrix of the transformer
102
103
104
105
106
107
10-10
10-8
10-6
10-4
10-2
100
102
Frequency(Hz)
Ad
mit
tan
ce(p
.u)
Admittance values for Three Phase Transformer
Actual
Fitted
102
103
104
105
106
107
-250
-200
-150
-100
-50
0
50
100
150
200
250
Frequency (Hz)
Adm
itta
nce
(S)
Phase values for Three Phase Transformer
Actual Values
Fitted Values
68
A congruently perfect fitting is obtained if the highest order of approximation is chosen. However,
this is not possible in practical applications. A higher order of approximation results in large element
size which in turn needs a sophisticated computational setup. The modeling technique presented in
this thesis, uses the order of approximation of N=23. This approximation order facilitates an
acceptable fitting and the rms error in the realized model in 1.3563%.
3.4 Summary
This chapter presented the high frequency modeling procedures of VCB, cable, and WTSU
Transformers. To simulate VCB model in PSCAD/EMTDC, a user defined black box model is
considered. A control strategy based VCB model cannot be used for simulating high frequency
transients, as it does not take into account mutual interaction of power system components.
Considering all high frequency parameters and statistical nature of arcing phenomenon, a high
frequency user defined black box model of VCB is created in PSCAD/EMTDC. The developed VCB
model is validated through a single-phase test circuit.
There are three models available for cables in PSCAD/EMTDC. For analyzing high frequency
switching transients the frequency dependent (phase) model should be used in PSCAD/EMTDC. The
cable model in PSCAD/EMTDC does not account for all the layer of a real cable therefore a cable
model is developed that can represent the high frequency phenomena of the real cable to the best
possible extent.
A high frequency black box model of WTSU transformer, within a frequency range of 20 Hz to 20
MHz is simulated in PSCAD/EMTDC. Black box model of actual transformer is developed because
the transformer terminal models available in literature are only valid for 0Hz - 250 kHz frequency
range.
These high frequency models are used to create a type IV wind farm (chapter 4) that serves as the
test bench for carrying out VCB initiated high frequency transient study on WTSU transformer of a
type IV wind farm.
69
Chapter 4
VCB initiated switching transient analysis on Type IV Wind Farm
In this chapter, a test bench (type IV wind farm) using the user defined high frequency black box
models of VCB, cable and WTSU transformer is outlined. Four different cases are defined where
switching transients generated due to opening and closing operation of VCB on low voltage side and
high voltage side of WTSU transformer are investigated. The VCB initiated switching transient study
is done in PSCAD/EMTDC.
4.1 Test Bench Layout
The test bench under consideration is a type-IV wind farm that is synchronized with the grid. Figure
4.1 shows the schematic of wind farm that has been designed in PSCAD/EMTDC.
Figure 4.1: Type IV wind turbine synchronized with the grid
The electrical system shown in Figure 4.1 is a single wind turbine generator synchronized with the
grid. As, the focus of this study is to investigate switching transients generated from the adjacent
VCBs of WTSU transformer, there are certain assumptions made during the development of this test
bench, are listed below:
The generation system is an approximated model of DFIG.
There is no significant impact of stator and rotor side converters on the magnitude of
switching transient overvoltages imposed on WTSU transformer. Hence, generic and
approximated stator and rotor converter models are used.
High frequency harmonic filters are not included in the test setup.
SVCs and STATCOMs do not affect the magnitude of switching transient overvoltages and
are not included in the test bench.
For the
included.
frequency
natural fr
overvoltag
WTSU tra
The fol
4.1.1 Ge
As the tes
model. Th
power con
with pitch
amount o
frequency
in the form
main fun
magnetiza
the bidire
Large dc l
e switching t
During the
y harmonics. A
requency of
ges when the
ansformer use
llowing sectio
neration Sy
st bench repli
he DFIG mo
nverters and n
h control of
of power. In t
y while fixed
m of generato
nction is to
ation and torq
ctional power
link capacitor
transient stud
energization
A voltage ma
the grid. S
e inrush curr
ed in this stud
ons describe th
ystem: Doub
icates the typ
odel (Figure 4
non-linear mu
rotor enables
the DIFG mo
frequency ele
or converter a
control the
que currents.
r flow. A gen
rs are used to
7
dy, the satura
of transform
agnification c
uch saturatio
rent of transf
dy includes th
he componen
bly fed indu
pe IV wind fa
4.2) is a stro
ulti-variable f
s variable sp
odel, the roto
ectrical power
and grid conv
voltage of th
These conve
neric control a
synchronize
Figure 4.2
70
ation characte
mer, heavy i
can take place
on characteri
former is inte
he transformer
nts of test ben
uction gene
arm, the gene
ongly coupled
feedback cont
peed operation
or of the gen
r is extracted
verter are used
he DC bus
erters require
algorithm is u
AC-DC-AC c
2: DFIG model
eristics of W
inrush curren
e if the resona
istic contribu
errupted. The
r saturation c
nch.
erator
eration system
d system incl
troller. Back t
n, which res
nerator is fed
from the stat
d in the mode
bar. Genera
two-stage po
used to contro
converter sys
l
WTSU transfo
nt that flows
ance frequenc
utes to the
e high freque
haracteristic.
m is an appro
luding induct
to back frequ
sults in gener
d with variab
tor. Back to b
el. The grid s
ator converter
ower conversi
ol the overall
stem.
ormer must b
s contains lo
cy matches th
high transien
ency model o
ximated DFI
tion generato
ency converte
ration of larg
le voltage an
back converter
side converter
r controls th
ion that allow
DFIG system
be
w
he
nt
of
G
or,
er
ge
nd
rs
r's
he
ws
m.
71
This DFIG design has the power converters built with two, three phase self-commutated back to
back PWM converters. The DC bus voltage regulation is taken care of by the intermediate capacitor
link. The dq frame representation of DFIG is given by following equations.
Equations for stator side of DIFG:
λds=‐Lstds+Lrtdr (4.1)
λqs = -Ls tqs + Lr tqr (4.2)
Vds = -Rs ids - ws λqs + (4.3)
Vdq = -Rs iqs - ws λds + (4.4)
Equations for rotor side of DIFG:
Vdr = Rr idr - sws λdr + (4.5)
Vqr = Rr iqr - sws λqr + (4.6)
Electrical output from the DFIG is given by:
Ps = (Vds ids+ Vqs iqs) (4.7)
Pr = (Vdr idr+ Vqr iqr) (4.8)
As, there is no power flow analysis or reactive power studies involved in this research, the reactive
power calculations and controllers for the generator and grid side converters are not elaborated in
detail. To understand the control strategies for the controllers in detail follow the reference [66].
4.1.2 Vacuum Circuit Breaker
High frequency black box modeling of VCB has been discussed in previous chapter. In the test bench,
the black box model of VCB is fed with physical parameters defined in chapter 3 for high and low
voltage connections.
As obse
model in P
C
R
T
R
C
Table 4-1
Type of VC
Medium
Voltage
Low Voltag
F
erved in Figu
PSCAD/EMT
Chopping curr
Rate of rise of
Transient recov
Rate of rise of
Current quench
outlines the p
B Cur
choppi
5
ge 5
Figure 4.3: Con
ure 4.3 the fo
TDC for diffe
rent
f dielectric stre
very voltage j
f quenching ca
hing capabilit
parameters ch
Table 4-1
rrent
ing (kA) d
5A
5A
7
nfiguration of b
ollowing five
erent voltage l
ength
just before cu
apability
ty of the brea
hosen for high
1: Properties of
Rate of rise o
dielectric stren
(kV/sec)
1.7e4
0.47e3
72
black box VCB
parameters a
levels:
urrent zero
ker
h and low vol
f VCB used in
of
ngth
Tran
reco
voltag
33
0.
B in PSCAD/EM
are the basis t
ltage VCBs in
the test bench
nsient
overy
ge (kV)
Ra
q
c
3.3
.69
MTDC
to define a b
n the test ben
h
ate of rise of
current
quenching
capability
(kA/sec2)
-3.4e7
1e8
lack box VC
nch.
Curren
quenchin
capabilit
(kA/sec
255e3
190e3
CB
nt
ng
ty
c)
4.1.3
The c
is 110
partic
freque
mode
The e
Table
Cable
cables used in
0 mm and m
cular entities
ency effects
l in PSCAD/E
entities of cab
Radius of
Resistivity
Relative pe
Permittivit
Capacitanc
Inductance
Surge imp
Wave trav
e 4-2 specifies
n the test benc
medium voltag
that are attr
of real cable
EMTDC.
Figure 4
le model in P
each layer of
y
ermittivity
ty
ce
e
edance
elling speed
s all the cable
ch are ABB X
ge side is 18
ributed to ca
e. Figure 4.4
4.4: Parameters
PSCAD\EMTD
f cable model
e parameters u
73
XLPE single c
80 mm. Cable
able model i
shows all th
s of cable mode
DC are as fol
used in the ca
core cables. T
e modeling d
in PSCAD/E
he physical p
el in PSCAD/E
llows:
able model of
The length of
discussed in
EMTDC, in
parameters ne
EMTDC
f the test bench
f low voltage
chapter 3, de
order to get
eeded by the
h.
cable
efined
t high
cable
74
Table 4-2: Cable model specifications
Radius
(mm)
Resistivity
(Ω.m)
Relative
Permittivity
Permittivity
(F/m)
Capacitance
(pF/m)
Inductance
(nH/m)
Wave
Travellin
g
Speed
(m/µsec)
r1 r2 r3 r4
5.6 12.6 13.6 16 2.82 × 10-8 2.3 8.854 × 10-12 217.54 160.5 179.3
4.1.4 WTSU Transformer
The transformer of the test bench is a 2.65 MVA, 690 V/33.3 kV WTSU transformer. As explained in
the previous chapter, a high frequency black box model of WTSU transformer is developed using
frequency dependent network equivalent (FDNE) in PSCAD/EMTDC.
The FDNE (Figure 4.5) represents the frequency dependent effects of transformer through rational
function approximation based models. The input to FDNE module is the transformer's port behavior
admittance matrix as a function of frequency. For the purpose of time domain simulations, the model
uses pole-residue form. Table 4-3 specifies the parameters used in the WTSU transformer model of
the test bench. Following curve fitting options are available in FDNE module:
Total number of ports
Maximum fitting error
Maximum order of fitting
Weighting factor for minimum to steady state frequency
Weighting factor for steady state frequency
Weighting factor for steady state to maximum frequency
Total num
por
3
4.1.5
The c
togeth
also k
The
imped
The
Theor
Table
mber of
rts
M
fi
Collection
collector grid
her representi
known as the
e value of th
dance indicate
short-circuit
retically, the s
Figu
e 4-3: WTSU t
Maximum
itting error
0.01%
grid
in the test b
ing the grid i
short circuit i
Fig
he impedance
es a stronger
current is o
strongest grid
ure 4.5: FDNE
transformer par
Maximu
order of fi
23
bench is mod
in PSCAD/EM
impedance is
gure 4.6: Collec
e represents t
grid. Therefo
often used i
d would occur
RRL
75
module and cu
rameters for FD
um
tting
W
fa
min
stea
fre
deled as a thr
MTDC, as sh
equal to 0.68
ction grid used
the strength
ore, the grid i
in many cas
r if the short-
L
urve fitting opt
DNE module i
Weighting
actor for
nimum to
ady state
equency
1
ree phase vol
hown in the F
8 + j6.78 Ω (4
d in the test ben
of the utility
s weaker if it
ses to descri
-circuit imped
tions
in PSCAD/EM
Weighting
factor for
steady stat
frequency
1
ltage source b
Figure 4.6. Th
4.9).
nch
y grid. A sm
t has a low sh
ibe the stren
dance is equal
Net
123
Equi
Freq
Depe
WTSU Tr
MTDC
g
te
y
Weig
facto
steady
max
freq
behind imped
he grid impe
maller value o
hort-circuit cu
ngth of the
l to zero and
twork
ivalent
456
quency
endent
ransformer
ghting
or for
y state to
ximum
uency
1
dance,
dance
of the
urrent.
grid.
short-
76
circuit current would be infinite. Pbase and Vbase selected for the shown collector grid is 100 MW and
33 kV respectively.
4.2 Tools for classifying the switching transients
The case studies subsequently presented in this chapter investigate following aspects of the switching
transients observed on the terminals of WTSU transformer:
Loading condition of the transformer
Peak voltage
Peak breaker current
Maximum rate of change of voltage
Frequency of oscillations
Number of reignitions
Figure 4.7: An example depicting different time regimes of transient waveform
The quantitative comparison of all the test cases will consider if the reignitions have occurred and
investigate the performance of the VCB once it has attained fully open or closed status. It is also
2 4 6 8 10 12 14
x 10-3
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Time in seconds
Tra
nsfo
rmer
ter
min
al V
olta
ge in
kV
Pre-event Reignition
period
Oscillatory
period
77
determined if the response of VCB (once an open or closed status is obtained) is oscillatory or not.
Figure 4.7 depicts different time regimes of a transient waveform.
There are four different frequency dependent behaviors that are observed in the VCB initiated
switching transients. First is the post transient voltage oscillation. This phenomenon of oscillatory
transients is observed once the transient period is over and switch is totally closed or open. The
electrical system resonates at one of the natural frequencies during these voltage oscillations. Second
phenomenon is re-strike which takes place at a frequency that is excited by the multiple reignitions
during the transient period. Third phenomenon is breakdown across the contact gap of the VCB. The
breakdown oscillations occur when the transient recovery voltage across the contact gap exceeds the
breakdown capability of the contact gap. The fourth and final phenomenon is cable reflections. The
frequency at which the cable reflections occur depends on the speed of propagation of the
electromagnetic waves in a particular cable and the length of the cable. Typical value for the
propagation speed of waves in cables is 200 m/µs but this value is different for each cable.
4.3 VCB initiated switching transient test cases
The following scenarios are carried out to analyze transient overvoltages in the proposed test bench:
VCB opening and closing on LV side of the WTSU transformer under no-load
VCB opening and closing on the LV side of the WTSU transformer under inductively load
VCB opening and closing on the HV side of the WTSU transformer under no-load
VCB opening and closing on the HV side of the WTSU transformer under inductively load
For all cases, the breaker operating time has been adjusted to match with the corresponding points
on the voltage waveform. The peak voltage and maximum rate of change of voltage are determined
from the time domain voltage waveform during restrike or prestrike periods. The frequency of
oscillations is determined by calculating the number of peaks from the start of oscillatory response
(approximately from 9 ms for this particular example as shown in Figure 4.7).
4.4 Elaboration of the test cases
This section of the chapter discusses the proposed test case scenarios.
78
4.4.1 Case I: VCB opening on LV side of WTSU transformer under no load
This simulation case shows the high frequency switching transients observed on the LV side of the
WTSU transformer during the opening operation of VCB. The selection of simulation time step is
very important for the transient simulations. It is observed that the simulation will not run if the
chosen time step is higher than 0.13 µsec.
Figure 4.8: Voltage waveform on LV side of WTSU transformer (not loaded)
The opening of the VCB takes place at 3 ms (Figure 4.8). No reignitions are observed, as the
voltage build up in form of transient recovery voltage across the breaker is not enough to exceed the
voltage withstand characteristics of the breaker.
Figure 4.9: Zoomed in view of voltage waveform at WTSU transformer LV terminal
0 5 10 15 20-1.5
-1
-0.5
0
0.5
1
1.5
2
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
2.5 3 3.5 4 4.5 5
-1
-0.5
0
0.5
1
1.5
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
2.95 3 3.05 3.1 3.15 3.2 3.25
-1
-0.5
0
0.5
1
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
79
Figure 4.9 shows the spikes observed during the period when the high frequency current tries to
establish an arc across the separating terminals of the VCB. As the voltage build up is not enough to
the support the arc and allow the high frequency current to flow, the current is eventually quenched
by the current quenching capability of the breaker. The synchronous oscillations observed in the post
transient waveform is because of the inductance of the generation system and the capacitance of the
LV cable. The post transient oscillations last for 18 ms. A close observation of the transient voltage
waveform suggests that there are no spikes observed in phase B (Red) during the transient period.
This phenomenon is attributed to the fact that there is no chopping current associated with the phase
B and the opening of the contacts for phase B takes at the natural current zero. Phase B exhibits zero
voltage build up during the transient period as no current is interrupted. Table 4-4 presents the
quantitative comparison of this case.
Table 4-4: Quantitative comparison of test case I
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
No load 1.4 0.07 ---- 0.59 ----
4.4.2 Case II: VCB opening on LV side of WTSU transformer under an inductive load
This scenario investigates transients on LV side of an inductively loaded WTSU transformer. The
transformer is loaded with 0.1Ω of inductive load. The value of the inductive load has been chosen in
accordance to IEEE Std. 57.142 and switching transient study analysis presented in [54] [55]. The
time step for this simulation scenario is kept 0.001 µsec, because of the high frequency steep front
reflective transients in transient phase of the voltage waveform. The reflections were observed in the
transient period during the reignitions when the time step is not appropriately chosen. The simulation
stopped abruptly when the time step is less than the 0.013 µsec because the compiler of
PSCAD/EMTDC is not able to calculate the distributed parameters of cable and transformer model
involved in the test bench.
80
Figure 4.10: Voltage waveform on LV side of WTSU transformer (loaded)
The phenomenon of opening VCB contacts starts at 2.5 ms (Figure 4.10). The major observation in
the scenario is that phase B (Red) exhibits only 5 reignitions. As mentioned earlier, the chopping
current in phase B is less as compared to the other two phases. Phase A and phase C exhibit 59 and 73
reignitions, respectively. The voltage oscillations die out in 19 ms.
The transient period lasts for 3.5 ms (Figure 4.10). The number of reignitions and the voltage build
up across the VCB contacts are fairly similar for phase A and phase C. Figure 4.11 shows the high
frequency reflective transients observed during the transient period. The highest frequency observed
during the transient period is 12.6 MHz. Table 4-5 presents the quantitative comparison of this case.
Figure 4.11: Zoomed in view of voltage waveform at WTSU transformer LV terminal
0 5 10 15 20 25-2
-1
0
1
2
3
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
2.2 2.4 2.6 2.8 3 3.2 3.4 3.6
-1.5
-1
-0.5
0
0.5
1
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
2.9 2.95 3 3.05 3.1-1.5
-1
-0.5
0
0.5
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
81
Table 4-5: Quantitative comparison of test case II
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
Inductive 3.5 0.09 7.5 0.47 73
4.4.3 Case III: VCB closing on LV side of WTSU transformer under no load
Figure 4.12: Voltage waveform on LV side of WTSU transformer (not loaded, closing)
With the closing operation of VCB, arises the problem of prestrikes. The case of closing the VCB on
LV side of WTSU transformer shows occurrence of no prestrikes. In comparison to the opening
operation under no load, closing operation exhibits high frequency voltage oscillations. The closing
operation of VCB takes place at 5 ms. Table 4-6 presents the quantitative comparison of this case.
Table 4-6: Quantitative comparison of test case III
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
No load 1.72 0.12 - 22.1 -
0 2 4 6 8 10 12 14 16-1
-0.5
0
0.5
1
1.5
Time in milliseconds(ms)
Tra
nsfo
rmer
term
ina
l Vo
ltag
e in
kV
82
4.4.4 Case IV: VCB closing on LV side of WTSU transformer under inductive load
The problem of prestrike gets pronounced during the inductive loading scenario of WTSU
transformer. During the closing operation of VCB on LV side of WTSU transformer, prestrikes are
observed in each phase of voltage waveform. This phenomenon is observed in Figure 4.13. The
number of prestrike is different for each phase, as the rate of rise of voltage at the instant of first
prestrike is different in each phase. The closing of vacuum circuit breaker takes place at 5.5 ms.
Highest number of reignitions is observed in phase B with 71 reignitions (Table 4-7). Phase A
observed 39 and phase C observed 21 reignitions, respectively. With regard to the oscillatory period,
which starts the post transient period, the oscillating frequency is 21 kHz. The oscillations die out in 3
ms.
Figure 4.13: Voltage waveform on LV side of WTSU transformer (loaded, closing)
The post transient voltage oscillations are dependent on the natural frequency of the electrical
circuit. Once the closing of VCB contacts takes place the configuration of the electrical system
changes. Hence, the post transient voltage oscillations observed during the opening and closing
operation of VCB are different.
0 5 10 15 20
-1
-0.5
0
0.5
1
1.5
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
83
Figure 4.14: Post transient voltage oscillations for case IV
Table 4-7: Quantitative comparison of test case IV
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
Inductive 2.1 0.09 1.1 20.3 71
4.4.5 Case V: VCB opening on HV side of WTSU transformer under no load
In contrast to case I, the opening operation on HV side of WTSU transformer shows some restrikes.
The rate of rise of voltage build up is 2.3 kV/µsec (Table 4-8), which does not exceed the withstand
capability of the contact gap for more than 4 times. The opening of vacuum circuit breaker takes
place at 1.5 ms. Highest number of reignitions is observed in phase B with 4 reignitions. Phase A
observed 2 and phase C observed 3 reignitions, respectively. The post transient voltage oscillations
die out in 6.5 ms.
5 5.2 5.4 5.6 5.8 6 6.2
-1
-0.5
0
0.5
1
1.5
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
84
Figure 4.15: Voltage waveform on HV side of WTSU transformer (not loaded)
As observed in the previous cases, chopping current is very low in one of the phases. Phase A
(black) with only two reignitions shows least magnitude of TRV (Figure 4.16).
Figure 4.16: Zoomed view of voltage waveform for case V
Table 4-8: Quantitative comparison of test case IV
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
No load 2.9 0.09 2.3 0.66 4
0 1 2 3 4 5-80
-60
-40
-20
0
20
40
60
80
100
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
1.4 1.5 1.6 1.7 1.8 1.9
-60
-40
-20
0
20
40
60
80
Time in milliseconds(ms)
Tra
nsf
orm
er
term
ina
l Vo
ltag
e in
kV
85
4.4.6 Case VI: VCB opening on HV side of WTSU transformer under inductive load
This scenario exhibits the highest peak voltage and maximum rate of rise of voltage for the voltage
waveforms observed at the WTSU transformer terminals. Figure 4.17 depicts all the three phases
exhibiting reignitions. The instant of VCB contact opening is 1.5 ms. The post transient voltage
oscillations die out in 4.5 ms. Phase C (black), observed the highest voltage peaks, because the
magnitude of recovery voltage across the contact gaps of the VCB is higher for phase C in
comparison to other two phases. Table 4-9 presents the quantitative comparison of this case. Highest
number of reignitions is observed in phase B with 74 reignitions. Phase A observed 56 and phase C
observed 62 reignitions, respectively.
Table 4-9: Quantitative comparison of test case VI
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
Inductive 3.03 0.73 28 0.56 74
Figure 4.17: Voltage waveform for case VI
0 1 2 3 4 5 6-150
-100
-50
0
50
100
150
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
86
Figure 4.18: Zoomed view depicting transient period for case VI voltage waveform
4.4.7 Case VII: VCB closing on HV side of WTSU transformer under no load
The results obtained for this case are similar to case III, where similar switching scenario is carried
on LV side. There is no reignition observed during the transient phase (Table 4-10). The frequency of
the post transient oscillations is similar to case III, as is the equivalent circuit after closing of VCB
terminals.
Closing of the VCB contacts start at 5 ms, resulting in voltage oscillations of 22 kHz, which die out
in 2 ms.
Figure 4.19: Voltage waveform on HV side of WTSU transformer (not loaded, closing)
1.4 1.6 1.8 2 2.2 2.4 2.6
-100
-50
0
50
100
Time in milliseconds(ms)
Tra
nsfo
rmer
term
inal V
oltag
e in
kV
0 2 4 6 8 10 12 14 16-60
-40
-20
0
20
40
60
80
Time in milliseconds(ms)
Tra
nsfo
rmer
term
inal V
oltag
e in
kV
87
Table 4-10: Quantitative comparison of test case VII
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
No load 1.8 0.17 ---- 22 ----
4.4.8 Case VIII: VCB closing on HV side of WTSU transformer under inductive load
High frequency steep front reflective transients are observed during VCB closing on HV side of
WTSU transformer under 0.1Ω inductive load. Simulation results (Figure 4.20) for this condition
show reignitions in all the three phases. The closing of vacuum circuit breaker takes place at 2.45 ms.
It is interesting to note that phase B (red) shows higher number of reignitions than the other two
phases (Figure 4.21). However, the magnitude of transient overvoltages is less in comparison to the
other two phases. Lower magnitude of TRV across phase B is governed by low chopping current in
phase B. Higher number of reignitions is observed because the stray inductance of the phase B
resonates with the impedance (capacitive part) of the collector grid, giving rise to higher number of
reignitions.
Figure 4.20: Voltage waveform across WTSU transformer terminals for case VIII
0 5 10 15-50
-40
-30
-20
-10
0
10
20
30
40
Time in milliseconds(ms)
Tra
ns
form
er
term
ina
l Vo
lta
ge
in k
V
88
Figure 4.21: Zoomed in voltage waveform depicting transient period
Table 4-11: Quantitative comparison of test case VIII
Transformer
loading
Peak voltage
(pu)
Peak breaker
current (kA)
Maximum rate
of change of
voltage
(kV/µsec)
Frequency of
oscillations
(kHz)
Number of
reignitions
Inductive 1.1 0.49 5.5 24 64
4.5 Summary
A test bench is proposed using user defined black box high frequency power system modules to
investigate VCB initiated transients. Six different attributes of voltage waveforms across the WTSU
transformer are used to investigate the transient behavior in eight different cases carried out on the
proposed test bench.
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6-40
-30
-20
-10
0
10
20
30
Time in milliseconds(ms)
Tra
nsfo
rmer
term
inal V
oltag
e in
kV
89
Chapter 5
Discussion
Voltage waveforms obtained from the VCB switching transient studies in Chapter 4 are used to
investigate the behavior of transients to which WTSU transformers are exposed under certain loading
conditions. Comparisons are made with earlier research work to highlight the relative differences and
contributions of the proposed work. The earlier research work includes switching transient studies on
different models of transformers and generic VCB models.
5.1 Investigation of VCB initiated transients on WTSU transformers
In this study, a new test bench is proposed to investigate VCB initiated high frequency transients
experienced at low and high voltage sides of WTSU transformers. The switching transient studies
carried out on the test bench elucidate the nature of the switching transients to which WTSU
transformers are exposed. Table 5-1 presents the quantitative comparison results for 8 cases that
contribute to the investigative transient study.
Table 5-1: Quantitative Comparison Results of Switching Transient Study
Case
No.
Peak Voltage
(pu)
Peak Breaker
Current (kA)
Maximum Rate of
Voltage Change
(kV/µsec)
Frequency of
Oscillations (kHz)
Number of
Reignitions
I 1.4 0.07 ---- 0.59 ----
II 3.5 0.09 7.5 0.47 73
III 1.72 0.12 - 22.1 -
IV 2.1 0.09 1.1 20.3 71
V 2.9 0.09 2.3 0.66 4
VI 3.03 0.73 28 0.56 74
VII 1.8 0.17 ---- 22 ----
VIII 1.1 0.49 5.5 24 64
During the transient period, five of the test cases exhibited reignitions in all three phases. As
expected, the cases with an inductively loaded WTSU transformer exhibited more severe switching
scenarios than did those with unloaded transformers. From these results, we can see that the TRV
across the VCB contacts is highly dependent on the configuration of external electrical circuits and
90
the magnitude of the chopping current. Since the magnitude of the chopping current here is different
for each phase, the linear time-dependent VCB voltage withstand capability and unusual TRVs along
each phase resulted in a different number of reignitions.
Compared to the opening operation, the closing operation of VCBs gave rise to much higher post-
transient frequency oscillations. The equivalent impedance of wind farm changes resulted in different
post-transient oscillations after the switching operation of VCBs. This phenomenon can be seen in
cases VI and VIII. In contrast to the frequency of 0.56 kHz exhibited during the opening of the VCB
on an inductively loaded WTSU transformer (case VI), the closing of the VCB (case VIII) exhibited a
post-transient oscillation frequency of 21 kHz.
The transient overvoltages observed in cases involving inductive load show a higher number of
reignitions because of the higher rate of voltage build-up. Furthermore, current that is quenched after
each reignition is different in loaded and unloaded transformers. This difference is evident in cases V
and VI, where the switching of unloaded and inductively loaded WTSU transformers is presented. In
both cases, the first reignition occurred at a peak voltage of 1.2 pu. After every reignition, the current
quenching capability of the breaker attempted to quench the high frequency current at the next zero
crossing, thereby resulting in fast-rising voltages across the VCB contacts. The interruption of high
frequency inductive current resulted in high TRV and caused 74 reignitions, as indicated in case VI.
In contrast, case V exhibited only 4 reignitions with no load current quenching.
Case VI, which shows the opening of a VCB on the HV side of a WTSU transformer under
inductive load, is recognized as the most onerous switching scenario. The voltage waveform captured
on the HV side of the WTSU transformer during the opening of the adjacent VCB under inductive
load depicts the highest rate of voltage rise during the transient period and also exhibits the maximum
peak voltage (Figure 5.1). Furthermore, the maximum number of reignitions is observed in this case.
91
Figure 5.1: Frequencies corresponding to different regimes of the transient period for case VI
5.2 Comparison of proposed VCB model with existing VCB model
The VCB model used in the proposed switching transient study incorporates the stochastic and
statistical nature of the vacuum arc. The VCB models available in previous research work do not take
into account the statistical nature of arcing time. The study by Gopal and Gajjar [67] provides a guide
that describes the dynamic modeling of VCB in PSCAD/EMTDC. Although the model presented in
this paper simulates the physical phenomena of VCB, the statistical nature of arcing time is not taken
into account. Their model has the following two limitations compared to the model presented in this
work:
It does not replicate the exact behaviour of prestrikes during the closing operations of VCB.
It does not describe the modeling strategy for a three-phase VCB, where the coordination
between three different phases is required to exactly replicate the real case switching
scenario.
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4
x 10-3
-150
-100
-50
0
50
100
150
Time in seconds
Tra
ns
form
er t
erm
ina
l Vo
ltag
e in
kV
1.795 1.8 1.805 1.81 1.815 1.82 1.825 1.83
x 10-3
-100
-50
0
50
Time in seconds
Tra
ns
form
er
term
ina
l Vo
ltag
e in
kV
10-10
10-5
100
105
1010
10-6
10-4
10-2
100
102
104
X: 3.35e+06Y: 54.45
Ma
gn
itu
de
of
Se
qu
en
ce
Imp
ed
an
ce
(oh
m)
Frequency in Hz10
-1010
-510
010
510
1010
-6
10-4
10-2
100
102
104
X: 1.722e+07Y: 23.47
Mag
nit
ud
e o
f S
equ
en
ce
Imp
eda
nc
e(o
hm
)
Frequency in Hz
Figure
once pres
physical p
the power
in Gopal
phenomen
Once
ideal beha
contacts a
The VC
nature of
Su
T
T
R
Pr
N
e 5.2 depicts
strikes occur
phenomenon
r frequency cu
and Gajjar's
na, which resu
the transient
avior of VCB
are fully open
CB model pre
arcing time:
uccessful inte
The current is
There are no re
Reigntions onl
restrikes take
No prestrikes s
the TRV and
r, there is no
of VCB. Onc
urrent, which
s VCB mode
ults in varied
t period is ov
is presented
ned once the tr
Figu
esented in thi
erruption only
not interrupte
eigntions at h
ly take place a
e place only at
should be obs
9
d current wav
o post-transie
ce the transien
h is finally qu
el because it
behavior of a
ver; the VCB
in Figure 3.1
ransient perio
ure 5.2: TRV a
s thesis incor
y takes place
ed at low arci
high arcing tim
at low arcing
t high closing
served at low
92
veforms in G
ent voltage
nt period is ov
enched at the
does not inc
arcing time.
B contacts are
3 (the model
od takes place
and current of V
rporate follow
at high arcing
ng times.
mes.
times.
g times.
arcing times.
Gopal and Gaj
oscillation, w
ver, the high
e next current
corporate hot
e either fully
presented in
e in the form o
VCB [67]
wing phenome
g times.
.
jjar's paper. A
which defies
frequency arc
t zero. This li
t and cold g
y open or ful
this thesis), w
of reignitions
ena to exhibi
As we can se
the real-tim
c still conduc
imitation exis
gap breakdow
ly closed. Th
where the VC
s.
it the statistic
e,
me
cts
sts
wn
he
CB
al
5.3 C
frequ
In thi
mode
Mir
uses p
wavef
Figur
Wor
Mirea[33
CurrWor
Compariso
uency tran
s section, a c
l and previou
reanue [33] p
power frequen
forms capture
e 5.3.
Figure 5.3:
Table
rk Test Ca
aneu ]
OpeningVCB o
HV sidetransfor
ent rk
OpeningVCB o
HV sidetransfor
on of result
nsformer m
omparison is
us research wo
presented swi
ncy transform
ed at the tran
: Voltage wave
5-2: Comparis
ase MaximFrequen
Conteg of on e of mer
181 kH
g of on e of mer
5MHz -MHz
ts with swi
model
drawn betwe
ork that uses t
itching transie
mer model and
sformer term
eform at a trans
on of Similar T
um ncy nt
ReflectiTransie
Hz Not observe
- 25 z
Observ
93
itching tran
een the presen
transformer m
ent study of
d π- model re
minals at the w
sformer termin
Test Cases from
ive ents
Observaof Volt
Oscillat
ed Limitedfade awatwo cyc
ved Observ
nsient ana
nted work us
model valid fo
a wind farm.
epresentation
wind farm (M
nal in Mireanue
m Mireaneu [3
ation tage tions
TransMo
d and ay in cles
UM(Po
frequtransf
moved Hi
frequblackmodorig
transf
alysis using
sing high freq
or power freq
. This switchi
of the cable.
Mireanue's the
e's wind farm s
3] and Current
former odel
CaM
MEC ower uency former
odel)
Π-m
igh uency k box del of ginal former
Phdepefreq
mo
g power
quency transfo
quency.
ing transient
One of the vo
sis) is presen
system [33]
t Work
able odel
Gene
Sys
model Vol
sou
hase-endent
quency odel
Doub
indu
gene
former
study
oltage
nted in
eration
stem
ltage
urce
bly-fed
uction
erator
It is obs
because th
scenario s
frequency
In the
transform
Figure 4
highest fr
interaction
componen
The com
The table
frequency
5.4 Prob
Choosin
subjects t
three-phas
reignition
Fig
Figure
the openi
served that th
he transforme
shown in Fig
y component o
proposed tes
mer model faci
4.18 shows a
equency com
n of power
nt predominan
mparison dra
illustrates th
y-dependent b
blem of ini
ng a synchro
that have not
se VCB mod
n.
gure 5.4: Overv
5.4 shows the
ing of VCB
he high freque
er and cable m
gure 5.3 isol
observed is 1
st bench, use
ilitate the obs
similar switc
mponents are o
system com
nt in reflectiv
awn from the
hat high frequ
behavior of sw
tial voltage
nized three-p
been dealt i
del, which do
voltage during
e three-phase
contacts is
9
ency effect of
models did n
ates one feed
81 kHz and re
e of a freque
ervation of hi
ching scenario
observed with
mponents, wh
ve transients is
observation
uency cable an
witching trans
e spike an
phase VCB m
in the literatu
oes not adequ
de-energizatio
voltage acro
different fo
94
f switching tra
ot take into a
der of a sim
eflective tran
ency-depende
igh frequency
o (case VI) in
hin a range of
hich are seen
s 14.75 MHz
of the two si
nd transforme
sients.
d synchro
model and obs
ure. The study
uately represe
on of LMF tran
oss the LMF t
or each phas
ansients in th
account high
mplified wind
nsients are not
ent cable mo
y reflective tra
n the proposed
f 5 MHz - 25
n at high fr
.
imilar test ca
er models are
onized thre
serving the in
dy by Shipp [
ent the initia
nsformer by the
transformer [6
se. This def
he wind farm
frequency ph
farm system
t observed.
odel and a h
ansients.
d wind farm t
MHz because
requencies. T
ases is shown
e required to
e-phase V
nitial voltage
[68] uses a d
al voltage spi
e vacuum brea
68]. Firstly, w
fies the real-
is not capture
henomena. Th
m. The highe
high frequenc
test bench. Th
e of the mutu
The frequenc
n in Table 5-2
investigate th
CB model
e spike are tw
desynchronize
ike needed fo
aker [68]
we can see th
-time physic
ed
he
est
cy
he
al
cy
2.
he
wo
ed
or
at
al
95
phenomena of the VCB contact gap opening, as the switching of the VCB contacts for all three
phases takes place at the same time. A distinct opening regime for each VCB phase is highlighted in
Figure 5.4, which shows that the three-phase VCB is not well coordinated.
Secondly, zero build-up voltage is observed during the contact gap opening, even though the
contact opening starts before the zero crossing. This accounts for the phenomenon of no reignition.
The transient recovery voltage across the VCB contacts is not included in Shipp's VCB model.
The two physical phenomena mentioned above have been dealt in the VCB model and switching
transient analysis presented in this thesis. The three-phase VCB model incorporates a control strategy
that synchronizes the three-phase VCB operation for the three distinct poles. The VCB model
includes the dielectric characteristics of the vacuum and recovery voltage of the breaker to account
for the initial build-up of voltage during the transient period (Figure 4.9). Both of these attributes of
the VCB model are discussed in Chapter 3.
5.5 WTSU Transformer model Validation
The WTSU transformer model is validated by comparing the voltage ratio (voltage transfer functions)
measured directly on the transformer terminals (as shown in Figure 5.5 and Figure 5.6) with the
calculated and simulated voltage ratios of the WTSU transformer model in PSCAD/EMTDC. The
voltage ratios calculated were obtained from the measured admittances as discussed in section 3.3.5
of chapter 3.
VHL (VHL14= ; VHL24 = ; VHL34 = )
Figure 5.5: Voltage ratios from high voltage side to low voltage side
1
2
3
4
5
6
VH1
VH2
VH3
VL4HV Side
LV Side
+ -
96
VLH (VLH41= ; VLH51 = ; VLH61 = )
Figure 5.6: Voltage ratios from high voltage to low voltage side
To validate the transformer model, six different voltage ratios were measured (equation 5.1) on the
transformer terminals and were compared with the calculated voltage ratios.
V14= ; V41 = ;V36 = ; V63 = ; V52 = ; V25 = (5.1)
The PSCAD/EMTDC WTSU transformer model is obtained by admittance matrix measurements
with 1201 frequency points. The order of rational function approximation used via vector fitting is 23.
Figure 5.7 compares the calculated voltage ratios with the corresponding simulated and measured
voltage ratios. It is observed that simulated voltage ratios reciprocate with the transfer characteristics
of measured voltage ratios. The small error observed in the low voltage segment is because of the
distinct zero sequence components of admittance values at low frequencies. Furthermore, Figure 5.7
shows that the simulated voltage ratios are in agreement with the calculated voltage ratios. As the
final transformer model is generated from the rational approximation of admittance matrix but not
from the real admittance matrix, a small deviation is observed between the simulated and calculated
admittances. This deviation between simulated and calculated voltage ratios accounts for the fitting
error observed in Figure 5.7. The WTSU transformer model is validated through the method of
comparison of measured, calculated and simulated voltage ratios.
1
2
3
4
5
6
VH1VL4
HV Side LV
Side+ -
VL5
VL6
97
Figure 5.7: Comparison of voltage ratios for measured, calculated and simulated values
5.6 Summary
A quantitative comparison of a VCB initiated switching transient analysis considering eight
switching scenarios inferred that a VCB opening on the HV side of a WTSU transformer under
inductive load (case VI) resulted in the most severe switching scenario. A detailed comparison of the
proposed models with previously published research work showed the need for incorporating the
physical attributes and high frequency phenomena of specific power system components during a
switching transient study. The chapter concludes with the validation of the WTSU transformer model
through voltage transfer function matching technique.
101
102
103
104
105
106
107
108
10-5
100
105
Frequency(Hz)
Vol
tage
Tra
nsf
er
Voltage Ratios on high and low voltage side of WTSU Transformer
Measured
Simulated
V41
V25
V52
V14
V36
V63
Calculated
98
Chapter 6
Conclusions and Future Work
6.1 Conclusions
The objective of this research study was to identify and develop high frequency black box models of
VCB, cable and WTSU transformer, alongwith conducting a VCB initiated switching transient study
on Type IV wind farm test bench.
The opening chapter reviewed wind technology and its development in Ontario's grid. It also
discussed typical configuration of wind farm generators and problems associated with WTSU
transformers. An overview of high frequency transients in wind farms and cable systems was
presented in the literature review section. Following this, modeling procedures of high frequency
model of VCB, frequency dependent phase model of cable and rational function approximation model
of an actual WTSU transformer were discussed. A single phase test circuit was established to realize
the statistical nature of arcing time and physical phenomena of VCB. The WTSU transformer model
was validated through voltage transfer function matching technique. Later these high frequency
models were used to formulate a test bench for investigating VCB initiated switching transients on
WTSU transformer. Lastly, the results of switching transient study were used to predict the behavior
of transient overvoltages experienced by WTSU transformers and identify the most severe switching
scenario. Based on the results of this work, the following conclusions can be drawn:
Internal overvoltages generated within the transformer due to switching transients, cannot be
computed using the PSCAD/EMTDC model. PSCAD/EMTDC generates an equivalent real
time RLC model of transformer, which is different from a detailed internal winding model of
transformer.
A VCB model that is able to simulate physical phenomena of vacuum gap and statistical
nature of arcing time with an ability of accurately representing overvoltages on the power
system components it interacts with is essential for switching transient analysis.
User defined black box models that can efficiently represent the frequency dependent
behaviour of cable and transformer, are necessary to capture the high frequency response of
electrical system to switching operations initiated by VCBs.
99
Of the eight test cases conducted during the switching transient study, opening of VCB on
HV side of WTSU transformer under inductive load is recognised as more severe switching
transient scenario.
Higher post transient frequency oscillations are observed during closing operation VCB
instead of opening operation.
In comparison to no load currents, interruption of high frequency inductive currents results in
higher magnitude of TRV (transient recovery voltage) leading to higher number of
reignitions.
6.2 Future Work
This work can be extended to address a number of distinct challenges. This section highlights some of
the important points.
6.2.1 Simulation and investigation of VCB initiated transients on whole wind farm
The test bench presented in this thesis comprises of single wind turbine synchronized with the grid.
Simulating whole wind farm as a test bench and analyzing effect of different wind farm configuration
on switching transients are important. Observation of variation in switching transients with addition
of multiple wind turbines to the proposed test bench is further required.
6.2.2 High frequency DFIG model studies
An advanced high frequency DFIG model will represent the switching transient more accurately.
Until now, inclusion of stator filter and grid inverter filter to existing DFIG model represents the high
frequency DFIG model. A discrete model representing frequency dependent characteristics of DFIG
is required to be developed and employed for switching transient studies.
6.2.3 High frequency harmonics in the wind farm
The focus of this research study was to investigate VCB initiated switching transients hence the
proposed test bench does not account for the high frequency harmonics generated from the converters
in the wind farm. As listed in chapter 1, high frequency harmonics from converters is identified as a
potential cause of WTSU transformer failures. This signifies the need of investigating converter
initiated high frequency harmonics in the wind farm. Incorporating sophisticated rotor and stator
converter controls with high frequency harmonic filters in the proposed test bench will facilitate the
100
analysis of high frequency harmonics experienced by WTSU transformer along with VCB initiated
switching transients.
6.2.4 Measurement setup for admittance matrix of transformer
The measurement of admittance matrix across the transformer terminals is a very time consuming
process because the connections are made every time a single element of admittance matrix or voltage
ratio is measured. During the WTSU transformer modeling procedure, 36 admittance elements and 9
voltage ratios were measured. In total 45 different connections were made, which was a time
consuming process. Also, background noise signals were observed while measuring the voltage
ratios. De-noising these unwanted signals increases the computational time of transformer model. An
adaptive measurement setup dedicated to measure the admittance matrix and voltage ratio, which
allow easy reconnection and de-noising will provide an alternative to an otherwise time consuming
procedure of transformer modeling.
101
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